Predicting NFL Stats

The goal of this capstone project was to set a baseline linear regression for predicting NFL statistics. The use of the analysis would be to project player performance and see if the team I am working with needs to consider making adjustments given various factors of the upcoming game/season.

Where to get the data

I went to the website http://armchairanalysis.com/data.php. I have a subscription to the database, so I connected into it via SQL. I downloaded the historical database onto my hard drive, and mapped it in MySQL.

I then queried the DB to get the fields I would need. This operation took extensive time, so once it ran, I exported to a csv file, then read the csv into R.

suppressMessages(library(dplyr))
## Warning: package 'dplyr' was built under R version 3.3.2
suppressMessages(library(tidyr))
## Warning: package 'tidyr' was built under R version 3.3.2
suppressMessages(library(ggplot2))
## Warning: package 'ggplot2' was built under R version 3.3.2
suppressMessages(library(reshape2))
## Warning: package 'reshape2' was built under R version 3.3.2
suppressMessages(library(caTools))
## Warning: package 'caTools' was built under R version 3.3.3
suppressMessages(library(caret))
## Warning: package 'caret' was built under R version 3.3.3
suppressMessages(library(GGally))
## Warning: package 'GGally' was built under R version 3.3.3
nfl_data <- read.csv("NFL_offense.csv")

The data is pretty clean from armchairanalyis, fivethirtyeight.com uses this website for its sports data, so it is a pretty reputable site.

I felt there were pieces of data either missing, or needing cleaning up. This brought on the fun process of cleaning and tidying the data.

Weather and field conditions

From a qualitative perspective, we know that field turf and ideal temperatures are the least inhibitive towards speed, according to players themselves. I wanted to identify extremes and hinderences.

I replaced all “NULL” temp fields with a generic “room” temperature assumption.

cold_weather and hot_weather were fields created to identify extreme ends of the temperature spectrum, and see if they have an impact on play

#make all null temperatures at game time "room" temperature
nfl_data$temp[nfl_data$temp == "NULL"] <- 70
nfl_data$temp <- as.integer(nfl_data$temp)

#highlight temp extremes
nfl_data <- mutate(nfl_data, cold_weather= ifelse(temp < 45, 1,0))
nfl_data <- mutate(nfl_data, hot_weather=  ifelse(temp > 85, 1,0))

#weather factors
nfl_data <- mutate(nfl_data, grass_1 = ifelse(surf == "DD GrassMaster" | surf == "Grass",
                                              1,0))
nfl_data <- mutate(nfl_data, bad_weather_1 = ifelse(cond == "Light Rain" | 
                                                      cond == "Rain" |
                                                      cond == "Flurries" |
                                                      cond == "Snow" |
                                                      cond == "Foggy" |
                                                      cond == "Windy" |
                                                      cond == "Hazy" |
                                                      cond == "Thunderstorms"|
                                                      cond == "Light Snow" |
                                                      cond == "Light Showers" ,1,0))

Home field advantage

Do players play better at home?

#identify home team
nfl_data$h <- as.character(nfl_data$h)
nfl_data$team <- as.character(nfl_data$team)
nfl_data <- mutate(nfl_data, home_team_1=  ifelse(h == team, 1,0))

Positions

Ignoring player stats, does the position matter

#identify position
nfl_data <- mutate(nfl_data, is_WR =  ifelse(pos1 == "WR", 1,0))
nfl_data <- mutate(nfl_data, is_TE =  ifelse(pos1 == "TE", 1,0))
nfl_data <- mutate(nfl_data, is_RB =  ifelse(pos1 == "RB", 1,0))
nfl_data <- mutate(nfl_data, is_QB =  ifelse(pos1 == "QB", 1,0))

Age

Every year players get older, so we want to know “Does father time impact player performance?”

#age
nfl_data <- mutate(nfl_data, age = year - yob)

Combine cleanup

The NFL combine is an event where prospective new players work out for the entire league to see. Their physical measurements are taken, and people find merit in this event. I wanted to see if these stats had any impact on player performance. Not all players attend the combine. For the fields where there are zeroes for the combine stat, I took the average for all non-zero stats for that position. This basically implies if you didn’t attend the combine, your stats are middle of the road.

#replace 0 forty with avg for position
nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(forty1 = ifelse(forty == 0, mean(forty[forty>0]), forty))
#replace 0 vertical with average for position
nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(vertical1 = ifelse(vertical == 0, mean(vertical[vertical>0]), vertical))
#replace 0 arm length with formula for 40% of height is arm
nfl_data$arm <- ifelse(nfl_data$arm == 0, nfl_data$height*0.4, nfl_data$arm)
nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(shuttle1 = ifelse(shuttle == 0, mean(shuttle[shuttle>0]), shuttle))
nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(cone1 = ifelse(cone == 0, mean(cone[cone>0]), cone))

NFL Teams

I created fields for teams (1 if player plays for that team in the header 0 if it doesn’t). I also cleaned up one team: The St Louis/LA Rams. The Rams moved in 2016 to LA, so the conditions of stadium changed. I combined the field into a single field.

#clean teams and give each team a field
nfl_data <- mutate(nfl_data, Teams =  ifelse(team == "STL" | team == "LA", "STL/LA",team))
nfl_data <- mutate(nfl_data, ARI = ifelse(Teams == "ARI",1,0))
nfl_data <- mutate(nfl_data, ATL = ifelse(Teams == "ATL",1,0))
nfl_data <- mutate(nfl_data, BAL = ifelse(Teams == "BAL",1,0))
nfl_data <- mutate(nfl_data, BUF = ifelse(Teams == "BUF",1,0))
nfl_data <- mutate(nfl_data, CAR = ifelse(Teams == "CAR",1,0))
nfl_data <- mutate(nfl_data, CHI = ifelse(Teams == "CHI",1,0))
nfl_data <- mutate(nfl_data, CIN = ifelse(Teams == "CIN",1,0))
nfl_data <- mutate(nfl_data, CLE = ifelse(Teams == "CLE",1,0))
nfl_data <- mutate(nfl_data, DAL = ifelse(Teams == "DAL",1,0))
nfl_data <- mutate(nfl_data, DEN = ifelse(Teams == "DEN",1,0))
nfl_data <- mutate(nfl_data, DET = ifelse(Teams == "DET",1,0))
nfl_data <- mutate(nfl_data, GB = ifelse(Teams == "GB",1,0))
nfl_data <- mutate(nfl_data, HOU = ifelse(Teams == "HOU",1,0))
nfl_data <- mutate(nfl_data, IND = ifelse(Teams == "IND",1,0))
nfl_data <- mutate(nfl_data, JAC = ifelse(Teams == "JAC",1,0))
nfl_data <- mutate(nfl_data, KC = ifelse(Teams == "KC",1,0))
nfl_data <- mutate(nfl_data, MIA = ifelse(Teams == "MIA",1,0))
nfl_data <- mutate(nfl_data, MINN = ifelse(Teams == "MIN",1,0))
nfl_data <- mutate(nfl_data, NE = ifelse(Teams == "NE",1,0))
nfl_data <- mutate(nfl_data, NOR = ifelse(Teams == "NO",1,0))
nfl_data <- mutate(nfl_data, NYG = ifelse(Teams == "NYG",1,0))
nfl_data <- mutate(nfl_data, NYJ = ifelse(Teams == "NYJ",1,0))
nfl_data <- mutate(nfl_data, OAK = ifelse(Teams == "OAK",1,0))
nfl_data <- mutate(nfl_data, PHI = ifelse(Teams == "PHI",1,0))
nfl_data <- mutate(nfl_data, PIT = ifelse(Teams == "PIT",1,0))
nfl_data <- mutate(nfl_data, SD = ifelse(Teams == "SD",1,0))
nfl_data <- mutate(nfl_data, SEA = ifelse(Teams == "SEA",1,0))
nfl_data <- mutate(nfl_data, SF = ifelse(Teams == "SF",1,0))
nfl_data <- mutate(nfl_data, STL = ifelse(Teams == "STL/LA",1,0))
nfl_data <- mutate(nfl_data, TB = ifelse(Teams == "TB",1,0))
nfl_data <- mutate(nfl_data, TEN = ifelse(Teams == "TEN",1,0))
nfl_data <- mutate(nfl_data, WAS = ifelse(Teams == "WAS",1,0))

Receiving Stats

For receiving, I wanted to get every players average: * yards * receptions * targets * touchdowns

I also wanted to get every position average, and average for team. Rationale for at least having that info is this: Compare player to team to league wide position

#calculate the averages by player, position, and team
#receiving
nfl_data <- nfl_data %>%
              group_by(player.1)%>%
                mutate(avg_recy_plyr = mean(recy))
nfl_data <- nfl_data %>%
              group_by(pos1)%>%
                mutate(avg_recy_pos = mean(recy))
nfl_data <- nfl_data %>%
              group_by(Teams)%>%
                mutate(avg_recy_team = mean(recy))
nfl_data <- nfl_data %>%
              group_by(player.1)%>%
                mutate(avg_rec_plyr = mean(rec))
nfl_data <- nfl_data %>%
              group_by(pos1)%>%
                mutate(avg_rec_pos = mean(rec))
nfl_data <- nfl_data %>%
              group_by(Teams)%>%
                mutate(avg_rec_team = mean(rec))
nfl_data <- nfl_data %>%
              group_by(player.1)%>%
                mutate(avg_trg_plyr = mean(trg))
nfl_data <- nfl_data %>%
              group_by(pos1)%>%
                mutate(avg_trg_pos = mean(trg))
nfl_data <- nfl_data %>%
              group_by(Teams)%>%
                mutate(avg_trg_team = mean(trg))
nfl_data <- nfl_data %>%
              group_by(player.1)%>%
                mutate(avg_rectd_plyr = mean(tdrec))
nfl_data <- nfl_data %>%
              group_by(pos1)%>%
                mutate(avg_rectd_pos = mean(tdrec))
nfl_data <- nfl_data %>%
              group_by(Teams)%>%
                mutate(avg_rectd_team = mean(tdrec))

Running Stats

I followed a similar process from up above.
The stats I was looking for the mean for were: * rushing attempts * rushing yards * fumbles

#running
nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_rbra_plyr = mean(ra))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_rbra_team = mean(ra))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_rbra_pos = mean(ra))

nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_rbry_plyr = mean(ry))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_rbry_team = mean(ry))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_rbry_pos = mean(ry))

nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_fuml_plyr = mean(fuml))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_fuml_team = mean(fuml))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_fuml_pos = mean(fuml))  

nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_tdr_plyr = mean(tdr))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_tdr_pos = mean(tdr))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_tdr_team = mean(tdr))

Passing

I followed a similar process from up above.
The stats I was looking for the mean for were: * passing yards * passing attempts * passing completions * passing touchdowns * interceptions

#passing
nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_qbpy_plyr = mean(py))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_qbpy_team = mean(py))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_qbpy_pos = mean(py))


nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_qbpc_plyr = mean(pc))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_qbpc_team = mean(pc))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_qbpc_pos = mean(pc))

nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_qbints_plyr = mean(ints))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_qbints_team = mean(ints))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_qbints_pos = mean(ints))

nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_qbtdp_plyr = mean(tdp))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_qbtdp_team = mean(tdp))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_qbtdp_pos = mean(tdp))

nfl_data <- nfl_data %>%
  group_by(player.1)%>%
  mutate(avg_qbpa_plyr = mean(pa))

nfl_data <- nfl_data %>%
  group_by(Teams)%>%
  mutate(avg_qbpa_team = mean(pa))

nfl_data <- nfl_data %>%
  group_by(pos1)%>%
  mutate(avg_qbpa_pos = mean(pa))

Pre-Analysis exploration

I wanted to learn a little about the data. I had approximately 100 fields to choose from, so it is hard to infer if there were any correlations or other patterns off hand. I built a subset of the fields I wanted to explore. I named this subset: nfl_data_fields

I then created a correlation matrix:

nfl_data_fields<- subset(nfl_data, select = c("height", "weight", "cold_weather", "hot_weather",
                         "home_team_1", "temp",
                         "forty1", "vertical1", "ARI", "ATL", "BAL", "BUF",
                         "CAR", "CHI", "CIN", "CLE", "DAL", "DEN", "DET", "GB", "HOU", "IND",
                         "JAC", "KC", "MIA", "MINN", "NE", "NOR", "NYG", "NYJ", "OAK", "PHI", "PIT",
                         "SD", "SEA", "STL", "TB", "TEN", "WAS",
                         "avg_recy_plyr","avg_recy_pos","avg_recy_team","avg_rec_plyr","avg_rec_pos",
                         "avg_rec_team", "avg_trg_plyr","avg_trg_pos","avg_trg_team","avg_rectd_plyr",
                         "avg_rectd_pos","avg_rectd_team","avg_tdr_plyr","avg_tdr_pos","avg_tdr_team",
                         "avg_rbra_plyr","avg_rbra_pos", "avg_rbra_team","avg_rbry_plyr","avg_rbry_pos",
                         "avg_rbry_team","avg_fuml_plyr","avg_fuml_pos", "avg_fuml_team","avg_qbpy_plyr",
                         "avg_qbpy_pos", "avg_qbpy_team","avg_qbpa_plyr","avg_qbpa_pos","avg_qbpa_team",
                         "avg_qbpc_plyr","avg_qbpc_pos", "avg_qbpc_team","avg_qbints_plyr", "avg_qbints_pos",
                         "avg_qbints_team","avg_qbtdp_plyr","avg_qbtdp_pos","avg_qbtdp_team","grass_1",
                         "bad_weather_1"))


cor_nfl <- cor(nfl_data_fields)

If you were to run cor_nfl, the print out is extremely difficult to read and gets cut off because of it’s size.

I decided a simpler view should be created, so I created an image of the matrix

image(cor_nfl)

This gives a pretty interesting view of the data, but is still hard to interpret. That being said, it was on the right path.

I then used qplot to get a better view of the data. With qplot I can control the colors, and since correlation matrices range from -1 to 1, setting the bookends of the color spectrum based on the values of the correlation would give me a very indicative heatmap

qplot(x=Var1, y=Var2, data=melt(cor(nfl_data_fields)), fill=value, geom="tile")+
  scale_fill_gradient2(limits=c(-1, 1))+
  theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 5),
        axis.text.y = element_text(size = 5))

There are strong relationships where we calculated general averages for the position, teams and players. That is not surprising since a stat like rushing will have strong relationships with how many attempts you make at rushing the ball. Typically, if you are running the ball more, you should see more yards. Obvious, but this confirms the correlation.

We then have to remove the highly correlated data fields.

highlyCor_nfl_data_fields1 <- findCorrelation(cor_nfl, cutoff = .8)
highlyCor_nfl_data_fields1
##  [1] 44 47 62 41 50 70 64 67 77 65 71 68 74 73 46 40 43 42 66 45 72 51 69
## [24] 53 60 56 52 55  6
highlyCor_nfl_data_fields2 <- findCorrelation(cor_nfl, cutoff = .85)
highlyCor_nfl_data_fields2
##  [1] 44 47 62 41 50 70 64 67 77 65 71 68 74 73 46 40 42 66 45 72 51 69 53
## [24] 60 56 52 55
highlyCor_nfl_data_fields3 <- findCorrelation(cor_nfl, cutoff = .9)
highlyCor_nfl_data_fields3
##  [1] 44 47 62 41 70 64 67 77 65 71 68 74 76 46 40 42 66 45 72 51 69 53 56
## [24] 52 55
filtered_nfl_data_fields <-nfl_data_fields
filtered_nfl_data_fields <- filtered_nfl_data_fields[,-highlyCor_nfl_data_fields1]
filtered_nfl_data_fields
## # A tibble: 39,255 × 51
##    height weight cold_weather hot_weather home_team_1   forty1 vertical1
##     <int>  <int>        <dbl>       <dbl>       <dbl>    <dbl>     <dbl>
## 1      73    217            0           0           0 4.400000  38.50000
## 2      70    209            0           0           0 4.550000  34.80631
## 3      73    190            0           0           0 4.580000  38.00000
## 4      74    225            0           0           0 4.794693  31.82285
## 5      72    189            0           0           1 4.410000  36.50000
## 6      72    209            0           0           1 4.830000  32.00000
## 7      71    200            0           0           1 4.410000  36.07315
## 8      75    248            0           0           1 4.670000  37.50000
## 9      73    190            0           0           0 4.463801  36.07315
## 10     72    180            0           0           0 4.463801  36.07315
## # ... with 39,245 more rows, and 44 more variables: ARI <dbl>, ATL <dbl>,
## #   BAL <dbl>, BUF <dbl>, CAR <dbl>, CHI <dbl>, CIN <dbl>, CLE <dbl>,
## #   DAL <dbl>, DEN <dbl>, DET <dbl>, GB <dbl>, HOU <dbl>, IND <dbl>,
## #   JAC <dbl>, KC <dbl>, MIA <dbl>, MINN <dbl>, NE <dbl>, NOR <dbl>,
## #   NYG <dbl>, NYJ <dbl>, OAK <dbl>, PHI <dbl>, PIT <dbl>, SD <dbl>,
## #   SEA <dbl>, STL <dbl>, TB <dbl>, TEN <dbl>, WAS <dbl>,
## #   avg_trg_team <dbl>, avg_rectd_plyr <dbl>, avg_tdr_team <dbl>,
## #   avg_rbra_team <dbl>, avg_rbry_plyr <dbl>, avg_rbry_pos <dbl>,
## #   avg_fuml_plyr <dbl>, avg_fuml_team <dbl>, avg_qbints_team <dbl>,
## #   avg_qbtdp_plyr <dbl>, avg_qbtdp_team <dbl>, grass_1 <dbl>,
## #   bad_weather_1 <dbl>
qplot(x=Var1, y=Var2, data=melt(cor(filtered_nfl_data_fields)), fill=value, geom="tile")+
  scale_fill_gradient2(limits=c(-1, 1))+
  theme(axis.text.x = element_text(angle = 90, hjust = 1, size = 5),
        axis.text.y = element_text(size = 5))

I tested cutoffs at 0.8, 0.85, 0.9 correlation, then removed the columns that were highly correlated at the 0.8 level.

Receiving Regressions

We have to set up our test and training data with preProcess:

set.seed(123)
split <- sample.split(nfl_data$recy, SplitRatio = 0.7)
TrainRecy <- subset(nfl_data, split == TRUE)
TestRecy <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(TrainRecy, method = c("center", "scale"))
trainTransformed <- predict(preProcValues, TrainRecy)
testTransformed <- predict(preProcValues, TestRecy)

We then inspect the relationships of the columns using ggpairs

ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("recy",colnames(filtered_nfl_data_fields[46:51]))])

Now that we are ready to train and test the data, let’s do it!

Receiving Yards first run

#formula for not having to write everything out

wrrecyregform <- formula(paste("recy ~ ", 
                         paste(colnames(filtered_nfl_data_fields), collapse="+")))

#first run of the recy regression
linRegrecy <- lm(wrrecyregform, data = trainTransformed)
summary(linRegrecy)
## 
## Call:
## lm(formula = wrrecyregform, data = trainTransformed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5035 -0.4258 -0.1162  0.2367  7.5163 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -3.166e-15  4.840e-03   0.000 1.000000    
## height           3.793e-03  9.391e-03   0.404 0.686273    
## weight          -6.979e-02  8.801e-03  -7.930 2.27e-15 ***
## cold_weather    -1.778e-02  5.095e-03  -3.490 0.000483 ***
## hot_weather     -6.230e-03  4.884e-03  -1.276 0.202139    
## home_team_1     -4.595e-03  5.266e-03  -0.873 0.382930    
## forty1          -4.717e-02  8.353e-03  -5.648 1.64e-08 ***
## vertical1        2.689e-03  6.422e-03   0.419 0.675408    
## ARI              2.401e-02  6.770e-03   3.547 0.000390 ***
## ATL              2.804e-02  6.803e-03   4.121 3.78e-05 ***
## BAL              2.715e-02  6.809e-03   3.988 6.69e-05 ***
## BUF              9.928e-03  6.721e-03   1.477 0.139647    
## CAR              2.115e-02  6.677e-03   3.168 0.001537 ** 
## CHI              2.497e-02  6.603e-03   3.782 0.000156 ***
## CIN              2.112e-02  6.724e-03   3.141 0.001683 ** 
## CLE              3.780e-02  6.693e-03   5.648 1.64e-08 ***
## DAL              1.258e-02  6.761e-03   1.860 0.062893 .  
## DEN              1.054e-02  6.787e-03   1.553 0.120447    
## DET              2.404e-02  6.694e-03   3.591 0.000330 ***
## GB              -1.135e-03  6.891e-03  -0.165 0.869180    
## HOU              2.902e-02  6.809e-03   4.262 2.03e-05 ***
## IND              1.928e-02  6.759e-03   2.853 0.004333 ** 
## JAC              1.586e-02  6.593e-03   2.406 0.016145 *  
## KC               2.082e-02  6.738e-03   3.090 0.002005 ** 
## MIA              2.199e-02  6.629e-03   3.317 0.000910 ***
## MINN             2.172e-02  6.670e-03   3.257 0.001128 ** 
## NE               1.683e-02  6.966e-03   2.416 0.015712 *  
## NOR              1.276e-02  6.945e-03   1.838 0.066058 .  
## NYG              2.344e-02  6.788e-03   3.453 0.000555 ***
## NYJ              1.344e-02  6.763e-03   1.987 0.046912 *  
## OAK              2.270e-02  6.805e-03   3.335 0.000853 ***
## PHI              2.565e-02  6.594e-03   3.889 0.000101 ***
## PIT              3.283e-02  6.768e-03   4.851 1.24e-06 ***
## SD               2.251e-02  6.641e-03   3.390 0.000701 ***
## SEA             -9.863e-04  6.892e-03  -0.143 0.886212    
## STL              2.074e-02  6.708e-03   3.091 0.001994 ** 
## TB               1.931e-02  6.645e-03   2.906 0.003662 ** 
## TEN              1.884e-02  6.686e-03   2.819 0.004826 ** 
## WAS              2.807e-02  6.721e-03   4.176 2.98e-05 ***
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr   5.388e-01  6.181e-03  87.171  < 2e-16 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr    4.959e-02  7.396e-03   6.704 2.06e-11 ***
## avg_rbry_pos    -7.121e-02  8.618e-03  -8.263  < 2e-16 ***
## avg_fuml_plyr   -6.954e-03  7.150e-03  -0.973 0.330717    
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -4.310e-02  7.766e-03  -5.550 2.88e-08 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -1.362e-02  5.569e-03  -2.446 0.014435 *  
## bad_weather_1   -9.516e-03  4.924e-03  -1.933 0.053285 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8024 on 27438 degrees of freedom
## Multiple R-squared:  0.3572, Adjusted R-squared:  0.3562 
## F-statistic: 338.9 on 45 and 27438 DF,  p-value: < 2.2e-16
#updating formula to take out insignigicant values
linRegrecy2 <- update(linRegrecy, ~. -height- hot_weather - home_team_1-vertical1-BUF-DAL-DEN-GB
                      -NE-NOR-NYJ-SEA
                      -avg_trg_team-avg_tdr_team-avg_rbra_team-avg_fuml_plyr-avg_fuml_team
                      -avg_qbints_plyr
                      -avg_qbints_team-avg_qbtdp_team-bad_weather1)
summary(linRegrecy2)
## 
## Call:
## lm(formula = recy ~ weight + cold_weather + forty1 + ARI + ATL + 
##     BAL + CAR + CHI + CIN + CLE + DET + HOU + IND + JAC + KC + 
##     MIA + MINN + NYG + OAK + PHI + PIT + SD + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1, data = trainTransformed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5054 -0.4250 -0.1179  0.2419  7.5182 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -2.958e-15  4.841e-03   0.000 1.000000    
## weight         -6.782e-02  6.074e-03 -11.166  < 2e-16 ***
## cold_weather   -1.826e-02  5.027e-03  -3.633 0.000281 ***
## forty1         -4.715e-02  7.051e-03  -6.688 2.31e-11 ***
## ARI             1.650e-02  5.038e-03   3.276 0.001055 ** 
## ATL             2.042e-02  5.046e-03   4.046 5.22e-05 ***
## BAL             1.901e-02  5.037e-03   3.774 0.000161 ***
## CAR             1.360e-02  5.061e-03   2.688 0.007196 ** 
## CHI             1.753e-02  5.039e-03   3.480 0.000503 ***
## CIN             1.302e-02  5.025e-03   2.592 0.009558 ** 
## CLE             3.025e-02  5.083e-03   5.952 2.68e-09 ***
## DET             1.641e-02  5.030e-03   3.262 0.001107 ** 
## HOU             2.169e-02  5.050e-03   4.295 1.76e-05 ***
## IND             1.164e-02  5.028e-03   2.315 0.020637 *  
## JAC             8.591e-03  5.054e-03   1.700 0.089151 .  
## KC              1.333e-02  5.089e-03   2.619 0.008814 ** 
## MIA             1.431e-02  5.038e-03   2.840 0.004509 ** 
## MINN            1.413e-02  5.034e-03   2.807 0.005003 ** 
## NYG             1.506e-02  5.029e-03   2.995 0.002748 ** 
## OAK             1.522e-02  5.107e-03   2.981 0.002877 ** 
## PHI             1.798e-02  5.034e-03   3.572 0.000355 ***
## PIT             2.492e-02  5.070e-03   4.915 8.93e-07 ***
## SD              1.471e-02  5.072e-03   2.900 0.003736 ** 
## STL             1.295e-02  5.044e-03   2.567 0.010260 *  
## TB              1.131e-02  5.055e-03   2.238 0.025231 *  
## TEN             1.124e-02  5.074e-03   2.216 0.026724 *  
## WAS             2.014e-02  5.065e-03   3.977 7.01e-05 ***
## avg_rectd_plyr  5.400e-01  6.058e-03  89.139  < 2e-16 ***
## avg_rbry_plyr   4.662e-02  6.950e-03   6.708 2.01e-11 ***
## avg_rbry_pos   -7.177e-02  7.494e-03  -9.577  < 2e-16 ***
## avg_qbtdp_plyr -4.698e-02  5.863e-03  -8.012 1.17e-15 ***
## grass_1        -1.750e-02  5.304e-03  -3.299 0.000971 ***
## bad_weather_1  -9.620e-03  4.917e-03  -1.957 0.050395 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8025 on 27451 degrees of freedom
## Multiple R-squared:  0.3567, Adjusted R-squared:  0.356 
## F-statistic: 475.8 on 32 and 27451 DF,  p-value: < 2.2e-16
#updating formulas to remove any insignificant values
linRegrecy3 <- update(linRegrecy2, ~. -JAC)
summary(linRegrecy3)
## 
## Call:
## lm(formula = recy ~ weight + cold_weather + forty1 + ARI + ATL + 
##     BAL + CAR + CHI + CIN + CLE + DET + HOU + IND + KC + MIA + 
##     MINN + NYG + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1, data = trainTransformed)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5044 -0.4254 -0.1184  0.2391  7.5200 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -2.937e-15  4.841e-03   0.000 1.000000    
## weight         -6.762e-02  6.073e-03 -11.134  < 2e-16 ***
## cold_weather   -1.885e-02  5.015e-03  -3.759 0.000171 ***
## forty1         -4.724e-02  7.051e-03  -6.701 2.11e-11 ***
## ARI             1.569e-02  5.016e-03   3.129 0.001756 ** 
## ATL             1.962e-02  5.024e-03   3.904 9.47e-05 ***
## BAL             1.819e-02  5.014e-03   3.628 0.000286 ***
## CAR             1.267e-02  5.031e-03   2.518 0.011819 *  
## CHI             1.667e-02  5.013e-03   3.324 0.000887 ***
## CIN             1.229e-02  5.007e-03   2.455 0.014086 *  
## CLE             2.934e-02  5.054e-03   5.805 6.52e-09 ***
## DET             1.563e-02  5.009e-03   3.121 0.001806 ** 
## HOU             2.085e-02  5.027e-03   4.149 3.36e-05 ***
## IND             1.087e-02  5.008e-03   2.171 0.029942 *  
## KC              1.237e-02  5.058e-03   2.446 0.014468 *  
## MIA             1.340e-02  5.010e-03   2.675 0.007469 ** 
## MINN            1.335e-02  5.013e-03   2.663 0.007741 ** 
## NYG             1.433e-02  5.010e-03   2.859 0.004248 ** 
## OAK             1.420e-02  5.072e-03   2.800 0.005108 ** 
## PHI             1.711e-02  5.008e-03   3.416 0.000636 ***
## PIT             2.404e-02  5.044e-03   4.766 1.89e-06 ***
## SD              1.377e-02  5.042e-03   2.730 0.006333 ** 
## STL             1.214e-02  5.021e-03   2.417 0.015636 *  
## TB              1.037e-02  5.025e-03   2.064 0.039052 *  
## TEN             1.028e-02  5.042e-03   2.038 0.041578 *  
## WAS             1.921e-02  5.036e-03   3.815 0.000136 ***
## avg_rectd_plyr  5.394e-01  6.049e-03  89.176  < 2e-16 ***
## avg_rbry_plyr   4.649e-02  6.950e-03   6.689 2.29e-11 ***
## avg_rbry_pos   -7.193e-02  7.494e-03  -9.600  < 2e-16 ***
## avg_qbtdp_plyr -4.723e-02  5.861e-03  -8.057 8.13e-16 ***
## grass_1        -1.649e-02  5.271e-03  -3.128 0.001760 ** 
## bad_weather_1  -9.828e-03  4.915e-03  -1.999 0.045573 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8025 on 27452 degrees of freedom
## Multiple R-squared:  0.3567, Adjusted R-squared:  0.356 
## F-statistic:   491 on 31 and 27452 DF,  p-value: < 2.2e-16

Modest gains in r-square and residual standard error and we cut the variables down to just 3. R2 is not very strong 0.4277. This is an improvement (slightly) over the historical average only as the explanatory variable.

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

RecyPredicted <- predict(linRegrecy3, newdata = testTransformed)

SSErecy <- sum((RecyPredicted - testTransformed$recy)^2)
SSTrecy <- sum((mean(nfl_data$recy)-testTransformed$recy)^2)
r2_recy <- 1 - SSErecy/SSTrecy 
r2_recy
## [1] 0.9989364
rmse_recy <- sqrt(SSErecy/nrow(testTransformed))
rmse_recy
## [1] 0.7763582

Looking at the regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegrecy3, which = c(1,2,3,5))

The residuals vs fitted appears to be okay for the model. The normal Q-Q looks okay, however, it may have some skewness to it. The scale-location does not seem to be ideal. The red line is not smooth, and there appears to be a gap in the data. The residuals vs leverage has some values that seem extreme.

The summary statistics are below.

confint(linRegrecy3)
##                        2.5 %        97.5 %
## (Intercept)    -0.0094882559  0.0094882559
## weight         -0.0795274473 -0.0557191232
## cold_weather   -0.0286793102 -0.0090208176
## forty1         -0.0610642220 -0.0334250908
## ARI             0.0058632903  0.0255259948
## ATL             0.0097682460  0.0294637762
## BAL             0.0083622071  0.0280189326
## CAR             0.0028054154  0.0225280288
## CHI             0.0068398849  0.0264926557
## CIN             0.0024791450  0.0221055179
## CLE             0.0194316899  0.0392452933
## DET             0.0058143275  0.0254512802
## HOU             0.0110002904  0.0307047052
## IND             0.0010562904  0.0206882581
## KC              0.0024557801  0.0222837058
## MIA             0.0035838450  0.0232233998
## MINN            0.0035260161  0.0231792969
## NYG             0.0045059231  0.0241468691
## OAK             0.0042619829  0.0241443427
## PHI             0.0072919585  0.0269223314
## PIT             0.0141504048  0.0339216782
## SD              0.0038833042  0.0236481674
## STL             0.0022968544  0.0219812473
## TB              0.0005210029  0.0202187408
## TEN             0.0003920961  0.0201581502
## WAS             0.0093422705  0.0290834158
## avg_rectd_plyr  0.5275582024  0.5512702914
## avg_rbry_plyr   0.0328656806  0.0601111735
## avg_rbry_pos   -0.0866224971 -0.0572471575
## avg_qbtdp_plyr -0.0587148793 -0.0357375061
## grass_1        -0.0268191284 -0.0061578226
## bad_weather_1  -0.0194620323 -0.0001935083
coef(summary(linRegrecy3))
##                     Estimate  Std. Error       t value     Pr(>|t|)
## (Intercept)    -2.937290e-15 0.004840822 -6.067751e-13 1.000000e+00
## weight         -6.762329e-02 0.006073396 -1.113435e+01 9.837517e-29
## cold_weather   -1.885006e-02 0.005014793 -3.758892e+00 1.710209e-04
## forty1         -4.724466e-02 0.007050617 -6.700783e+00 2.113140e-11
## ARI             1.569464e-02 0.005015867  3.128999e+00 1.755866e-03
## ATL             1.961601e-02 0.005024241  3.904274e+00 9.473462e-05
## BAL             1.819057e-02 0.005014342  3.627708e+00 2.864663e-04
## CAR             1.266672e-02 0.005031150  2.517660e+00 1.181939e-02
## CHI             1.666627e-02 0.005013333  3.324389e+00 8.872841e-04
## CIN             1.229233e-02 0.005006599  2.455226e+00 1.408576e-02
## CLE             2.933849e-02 0.005054361  5.804590e+00 6.523318e-09
## DET             1.563280e-02 0.005009298  3.120757e+00 1.805735e-03
## HOU             2.085250e-02 0.005026507  4.148507e+00 3.356579e-05
## IND             1.087227e-02 0.005008026  2.170970e+00 2.994199e-02
## KC              1.236974e-02 0.005058014  2.445573e+00 1.446845e-02
## MIA             1.340362e-02 0.005009962  2.675394e+00 7.468569e-03
## MINN            1.335266e-02 0.005013463  2.663360e+00 7.740977e-03
## NYG             1.432640e-02 0.005010317  2.859379e+00 4.247906e-03
## OAK             1.420316e-02 0.005071900  2.800363e+00 5.108079e-03
## PHI             1.710714e-02 0.005007619  3.416223e+00 6.358817e-04
## PIT             2.403604e-02 0.005043563  4.765687e+00 1.891737e-06
## SD              1.376574e-02 0.005041927  2.730253e+00 6.332615e-03
## STL             1.213905e-02 0.005021400  2.417464e+00 1.563557e-02
## TB              1.036987e-02 0.005024804  2.063737e+00 3.905207e-02
## TEN             1.027512e-02 0.005042231  2.037813e+00 4.157822e-02
## WAS             1.921284e-02 0.005035877  3.815193e+00 1.363745e-04
## avg_rectd_plyr  5.394142e-01 0.006048847  8.917638e+01 0.000000e+00
## avg_rbry_plyr   4.648843e-02 0.006950202  6.688788e+00 2.293467e-11
## avg_rbry_pos   -7.193483e-02 0.007493516 -9.599609e+00 8.683028e-22
## avg_qbtdp_plyr -4.722619e-02 0.005861424 -8.057119e+00 8.125991e-16
## grass_1        -1.648848e-02 0.005270606 -3.128383e+00 1.759546e-03
## bad_weather_1  -9.827770e-03 0.004915313 -1.999419e+00 4.557289e-02
anova(linRegrecy3)
## Analysis of Variance Table
## 
## Response: recy
##                   Df  Sum Sq Mean Sq    F value    Pr(>F)    
## weight             1   286.5   286.5   444.7939 < 2.2e-16 ***
## cold_weather       1    17.7    17.7    27.4087 1.659e-07 ***
## forty1             1  1096.0  1096.0  1701.7895 < 2.2e-16 ***
## ARI                1     1.6     1.6     2.4409 0.1182194    
## ATL                1    22.2    22.2    34.5178 4.272e-09 ***
## BAL                1     0.0     0.0     0.0026 0.9592773    
## CAR                1     3.4     3.4     5.2935 0.0214132 *  
## CHI                1     0.0     0.0     0.0001 0.9922825    
## CIN                1     0.0     0.0     0.0696 0.7919203    
## CLE                1     1.6     1.6     2.4396 0.1183183    
## DET                1    13.6    13.6    21.1018 4.375e-06 ***
## HOU                1     0.8     0.8     1.2155 0.2702583    
## IND                1     1.2     1.2     1.9041 0.1676280    
## KC                 1    13.8    13.8    21.3793 3.785e-06 ***
## MIA                1     0.1     0.1     0.1325 0.7158119    
## MINN               1     8.8     8.8    13.6466 0.0002211 ***
## NYG                1     7.1     7.1    11.0093 0.0009078 ***
## OAK                1    12.5    12.5    19.3499 1.092e-05 ***
## PHI                1     1.5     1.5     2.3813 0.1228075    
## PIT                1    10.1    10.1    15.6244 7.745e-05 ***
## SD                 1     8.7     8.7    13.5839 0.0002286 ***
## STL                1     3.6     3.6     5.6376 0.0175859 *  
## TB                 1     0.9     0.9     1.3868 0.2389488    
## TEN                1     6.5     6.5    10.0632 0.0015142 ** 
## WAS                1     2.1     2.1     3.2224 0.0726498 .  
## avg_rectd_plyr     1  8183.3  8183.3 12705.9907 < 2.2e-16 ***
## avg_rbry_plyr      1     0.1     0.1     0.2085 0.6479341    
## avg_rbry_pos       1    47.9    47.9    74.4186 < 2.2e-16 ***
## avg_qbtdp_plyr     1    42.0    42.0    65.1375 7.268e-16 ***
## grass_1            1     6.5     6.5    10.1376 0.0014544 ** 
## bad_weather_1      1     2.6     2.6     3.9977 0.0455729 *  
## Residuals      27452 17680.4     0.6                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

I would say overall, the model is just okay for predicting. The average yards receiving historical for the player is really the best predictor according to this analysis

Now we inspect the AIC:

#aic 
aic_recy <- step(lm(wrrecyregform, data = trainTransformed), direction = "backward")
## Start:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12056.38
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - SEA             1       0.0 17665 -12058.4
## - GB              1       0.0 17665 -12058.4
## - height          1       0.1 17665 -12058.2
## - vertical1       1       0.1 17665 -12058.2
## - home_team_1     1       0.5 17666 -12057.6
## - avg_fuml_plyr   1       0.6 17666 -12057.4
## - hot_weather     1       1.0 17666 -12056.8
## <none>                        17665 -12056.4
## - BUF             1       1.4 17666 -12056.2
## - DEN             1       1.6 17667 -12056.0
## - NOR             1       2.2 17667 -12055.0
## - DAL             1       2.2 17667 -12054.9
## - bad_weather_1   1       2.4 17667 -12054.6
## - NYJ             1       2.5 17668 -12054.4
## - JAC             1       3.7 17669 -12052.6
## - NE              1       3.8 17669 -12052.5
## - grass_1         1       3.9 17669 -12052.4
## - TEN             1       5.1 17670 -12050.4
## - IND             1       5.2 17670 -12050.2
## - TB              1       5.4 17671 -12049.9
## - KC              1       6.1 17671 -12048.8
## - STL             1       6.2 17671 -12048.8
## - CIN             1       6.4 17671 -12048.5
## - CAR             1       6.5 17672 -12048.3
## - MINN            1       6.8 17672 -12047.8
## - MIA             1       7.1 17672 -12047.4
## - OAK             1       7.2 17672 -12047.2
## - SD              1       7.4 17672 -12046.9
## - NYG             1       7.7 17673 -12046.4
## - cold_weather    1       7.8 17673 -12046.2
## - ARI             1       8.1 17673 -12045.8
## - DET             1       8.3 17673 -12045.5
## - CHI             1       9.2 17674 -12044.1
## - PHI             1       9.7 17675 -12043.2
## - BAL             1      10.2 17675 -12042.5
## - ATL             1      10.9 17676 -12041.4
## - WAS             1      11.2 17676 -12040.9
## - HOU             1      11.7 17677 -12040.2
## - PIT             1      15.1 17680 -12034.8
## - avg_qbtdp_plyr  1      19.8 17685 -12027.5
## - forty1          1      20.5 17686 -12026.5
## - CLE             1      20.5 17686 -12026.5
## - avg_rbry_plyr   1      28.9 17694 -12013.4
## - weight          1      40.5 17706 -11995.5
## - avg_rbry_pos    1      44.0 17709 -11990.1
## - avg_rectd_plyr  1    4892.2 22557  -5339.4
## 
## Step:  AIC=-12058.36
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - GB              1       0.0 17665 -12060.4
## - height          1       0.1 17665 -12060.2
## - vertical1       1       0.1 17665 -12060.2
## - home_team_1     1       0.5 17666 -12059.6
## - avg_fuml_plyr   1       0.6 17666 -12059.4
## - hot_weather     1       1.1 17666 -12058.7
## <none>                        17665 -12058.4
## - BUF             1       2.1 17667 -12057.1
## - DEN             1       2.3 17667 -12056.8
## - bad_weather_1   1       2.4 17668 -12056.6
## - DAL             1       3.2 17668 -12055.4
## - NOR             1       3.2 17668 -12055.4
## - NYJ             1       3.7 17669 -12054.6
## - grass_1         1       3.9 17669 -12054.4
## - JAC             1       5.1 17670 -12052.4
## - NE              1       5.4 17671 -12051.9
## - TEN             1       7.1 17672 -12049.4
## - IND             1       7.4 17672 -12048.9
## - TB              1       7.5 17673 -12048.7
## - cold_weather    1       7.9 17673 -12048.0
## - KC              1       8.5 17674 -12047.1
## - STL             1       8.5 17674 -12047.1
## - CAR             1       8.9 17674 -12046.5
## - CIN             1       8.9 17674 -12046.4
## - MINN            1       9.5 17675 -12045.6
## - MIA             1       9.7 17675 -12045.3
## - OAK             1       9.9 17675 -12045.0
## - SD              1      10.0 17675 -12044.8
## - NYG             1      10.8 17676 -12043.5
## - ARI             1      11.2 17676 -12042.9
## - DET             1      11.4 17677 -12042.6
## - CHI             1      12.5 17678 -12041.0
## - PHI             1      13.2 17678 -12039.8
## - BAL             1      14.4 17680 -12037.9
## - ATL             1      15.1 17680 -12036.9
## - WAS             1      15.4 17681 -12036.4
## - HOU             1      16.1 17681 -12035.3
## - avg_qbtdp_plyr  1      19.9 17685 -12029.5
## - forty1          1      20.5 17686 -12028.5
## - PIT             1      20.8 17686 -12028.0
## - CLE             1      27.7 17693 -12017.2
## - avg_rbry_plyr   1      28.9 17694 -12015.4
## - weight          1      40.5 17706 -11997.4
## - avg_rbry_pos    1      44.0 17709 -11992.1
## - avg_rectd_plyr  1    4892.2 22557  -5341.4
## 
## Step:  AIC=-12060.35
## recy ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - height          1       0.1 17665 -12062.2
## - vertical1       1       0.1 17665 -12062.2
## - home_team_1     1       0.5 17666 -12061.6
## - avg_fuml_plyr   1       0.6 17666 -12061.4
## - hot_weather     1       1.1 17666 -12060.7
## <none>                        17665 -12060.4
## - BUF             1       2.4 17668 -12058.6
## - bad_weather_1   1       2.4 17668 -12058.6
## - DEN             1       2.7 17668 -12058.2
## - DAL             1       3.7 17669 -12056.6
## - NOR             1       3.7 17669 -12056.5
## - grass_1         1       3.9 17669 -12056.3
## - NYJ             1       4.2 17669 -12055.8
## - JAC             1       5.9 17671 -12053.2
## - NE              1       6.3 17671 -12052.5
## - cold_weather    1       8.0 17673 -12049.9
## - TEN             1       8.1 17673 -12049.8
## - IND             1       8.4 17674 -12049.3
## - TB              1       8.6 17674 -12049.0
## - STL             1       9.6 17675 -12047.4
## - KC              1       9.8 17675 -12047.1
## - CIN             1      10.2 17675 -12046.5
## - CAR             1      10.2 17675 -12046.5
## - MINN            1      10.7 17676 -12045.7
## - MIA             1      11.1 17676 -12045.1
## - OAK             1      11.3 17676 -12044.7
## - SD              1      11.5 17677 -12044.5
## - NYG             1      12.4 17677 -12043.1
## - ARI             1      12.7 17678 -12042.6
## - DET             1      12.9 17678 -12042.2
## - CHI             1      14.2 17679 -12040.3
## - PHI             1      15.0 17680 -12039.0
## - BAL             1      16.5 17682 -12036.7
## - ATL             1      17.1 17682 -12035.8
## - WAS             1      17.6 17683 -12035.0
## - HOU             1      18.2 17683 -12034.0
## - avg_qbtdp_plyr  1      19.9 17685 -12031.4
## - forty1          1      20.5 17686 -12030.4
## - PIT             1      23.9 17689 -12025.2
## - avg_rbry_plyr   1      28.9 17694 -12017.4
## - CLE             1      31.4 17697 -12013.5
## - weight          1      40.5 17706 -11999.4
## - avg_rbry_pos    1      44.0 17709 -11993.9
## - avg_rectd_plyr  1    4928.2 22593  -5299.6
## 
## Step:  AIC=-12062.19
## recy ~ weight + cold_weather + hot_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - vertical1       1       0.1 17665 -12064.0
## - home_team_1     1       0.5 17666 -12063.4
## - avg_fuml_plyr   1       0.6 17666 -12063.3
## - hot_weather     1       1.1 17666 -12062.5
## <none>                        17665 -12062.2
## - bad_weather_1   1       2.4 17668 -12060.4
## - BUF             1       2.5 17668 -12060.3
## - DEN             1       2.7 17668 -12060.0
## - DAL             1       3.7 17669 -12058.4
## - NOR             1       3.8 17669 -12058.3
## - grass_1         1       3.9 17669 -12058.1
## - NYJ             1       4.3 17669 -12057.5
## - JAC             1       5.9 17671 -12055.0
## - NE              1       6.3 17671 -12054.4
## - cold_weather    1       8.0 17673 -12051.7
## - TEN             1       8.2 17673 -12051.5
## - IND             1       8.4 17674 -12051.1
## - TB              1       8.6 17674 -12050.8
## - STL             1       9.7 17675 -12049.1
## - KC              1       9.9 17675 -12048.8
## - CAR             1      10.2 17675 -12048.3
## - CIN             1      10.3 17676 -12048.1
## - MINN            1      10.9 17676 -12047.2
## - MIA             1      11.2 17676 -12046.8
## - SD              1      11.6 17677 -12046.1
## - OAK             1      11.7 17677 -12046.0
## - NYG             1      12.5 17678 -12044.8
## - ARI             1      12.9 17678 -12044.2
## - DET             1      13.0 17678 -12044.0
## - CHI             1      14.5 17680 -12041.7
## - PHI             1      15.1 17680 -12040.8
## - BAL             1      16.6 17682 -12038.4
## - ATL             1      17.1 17682 -12037.6
## - WAS             1      17.5 17683 -12037.0
## - HOU             1      18.5 17684 -12035.5
## - forty1          1      20.5 17686 -12032.3
## - avg_qbtdp_plyr  1      20.6 17686 -12032.2
## - PIT             1      24.0 17689 -12026.9
## - avg_rbry_plyr   1      29.0 17694 -12019.1
## - CLE             1      31.6 17697 -12015.1
## - avg_rbry_pos    1      60.4 17726 -11970.3
## - weight          1      76.5 17742 -11945.5
## - avg_rectd_plyr  1    4988.4 22654  -5228.3
## 
## Step:  AIC=-12064
## recy ~ weight + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - home_team_1     1       0.5 17666 -12065.2
## - avg_fuml_plyr   1       0.6 17666 -12065.1
## - hot_weather     1       1.1 17666 -12064.4
## <none>                        17665 -12064.0
## - bad_weather_1   1       2.4 17668 -12062.3
## - BUF             1       2.4 17668 -12062.2
## - DEN             1       2.7 17668 -12061.8
## - DAL             1       3.7 17669 -12060.2
## - NOR             1       3.8 17669 -12060.1
## - grass_1         1       3.9 17669 -12059.9
## - NYJ             1       4.4 17670 -12059.2
## - JAC             1       6.0 17671 -12056.6
## - NE              1       6.3 17672 -12056.2
## - cold_weather    1       8.0 17673 -12053.5
## - TEN             1       8.2 17674 -12053.2
## - IND             1       8.5 17674 -12052.9
## - TB              1       8.6 17674 -12052.6
## - STL             1       9.7 17675 -12050.9
## - KC              1       9.9 17675 -12050.6
## - CAR             1      10.3 17676 -12050.0
## - CIN             1      10.3 17676 -12050.0
## - MINN            1      11.1 17676 -12048.8
## - MIA             1      11.1 17676 -12048.7
## - OAK             1      11.6 17677 -12047.9
## - SD              1      11.6 17677 -12047.9
## - NYG             1      12.5 17678 -12046.6
## - ARI             1      12.8 17678 -12046.0
## - DET             1      13.1 17678 -12045.6
## - CHI             1      14.4 17680 -12043.6
## - PHI             1      15.0 17680 -12042.7
## - BAL             1      16.6 17682 -12040.3
## - ATL             1      17.0 17682 -12039.6
## - WAS             1      17.5 17683 -12038.8
## - HOU             1      18.6 17684 -12037.1
## - avg_qbtdp_plyr  1      20.6 17686 -12034.0
## - PIT             1      24.0 17689 -12028.7
## - avg_rbry_plyr   1      28.9 17694 -12021.1
## - forty1          1      30.5 17696 -12018.6
## - CLE             1      31.8 17697 -12016.6
## - avg_rbry_pos    1      60.7 17726 -11971.7
## - weight          1      76.9 17742 -11946.6
## - avg_rectd_plyr  1    5002.4 22668  -5213.2
## 
## Step:  AIC=-12065.24
## recy ~ weight + cold_weather + hot_weather + forty1 + ARI + ATL + 
##     BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU + 
##     IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - avg_fuml_plyr   1       0.6 17666 -12066.3
## - hot_weather     1       1.0 17667 -12065.6
## <none>                        17666 -12065.2
## - BUF             1       2.4 17668 -12063.4
## - bad_weather_1   1       2.5 17668 -12063.4
## - DEN             1       2.7 17669 -12063.0
## - NOR             1       4.0 17670 -12061.0
## - DAL             1       4.2 17670 -12060.8
## - NYJ             1       4.3 17670 -12060.5
## - grass_1         1       4.4 17670 -12060.3
## - JAC             1       6.0 17672 -12057.9
## - NE              1       6.2 17672 -12057.6
## - TEN             1       8.2 17674 -12054.4
## - cold_weather    1       8.3 17674 -12054.3
## - TB              1       8.6 17674 -12053.9
## - IND             1       9.0 17675 -12053.2
## - KC              1       9.9 17676 -12051.8
## - CIN             1      10.3 17676 -12051.3
## - CAR             1      10.3 17676 -12051.3
## - STL             1      10.3 17676 -12051.2
## - MINN            1      11.1 17677 -12049.9
## - MIA             1      11.1 17677 -12049.9
## - SD              1      11.7 17677 -12049.1
## - OAK             1      11.7 17678 -12049.1
## - NYG             1      12.4 17678 -12047.9
## - DET             1      13.7 17680 -12045.9
## - ARI             1      13.8 17680 -12045.8
## - CHI             1      14.4 17680 -12044.8
## - PHI             1      15.0 17681 -12043.8
## - BAL             1      16.5 17682 -12041.6
## - WAS             1      17.5 17683 -12040.0
## - ATL             1      18.1 17684 -12039.1
## - HOU             1      19.8 17686 -12036.5
## - avg_qbtdp_plyr  1      20.6 17686 -12035.3
## - PIT             1      24.0 17690 -12029.9
## - avg_rbry_plyr   1      28.9 17695 -12022.3
## - forty1          1      30.4 17696 -12019.9
## - CLE             1      31.8 17698 -12017.8
## - avg_rbry_pos    1      60.7 17727 -11973.0
## - weight          1      76.9 17743 -11947.8
## - avg_rectd_plyr  1    5002.6 22668  -5214.3
## 
## Step:  AIC=-12066.32
## recy ~ weight + cold_weather + hot_weather + forty1 + ARI + ATL + 
##     BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU + 
##     IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - hot_weather     1       1.0 17667 -12066.7
## <none>                        17666 -12066.3
## - BUF             1       2.3 17669 -12064.7
## - bad_weather_1   1       2.4 17669 -12064.5
## - DEN             1       2.6 17669 -12064.2
## - NOR             1       4.0 17670 -12062.0
## - DAL             1       4.1 17671 -12061.9
## - NYJ             1       4.2 17671 -12061.8
## - grass_1         1       4.4 17671 -12061.4
## - JAC             1       6.0 17672 -12059.0
## - NE              1       6.4 17673 -12058.4
## - TEN             1       8.0 17674 -12055.8
## - cold_weather    1       8.2 17675 -12055.5
## - TB              1       8.4 17675 -12055.2
## - IND             1       8.9 17675 -12054.5
## - KC              1       9.8 17676 -12053.0
## - STL             1      10.1 17677 -12052.6
## - CIN             1      10.1 17677 -12052.5
## - CAR             1      10.1 17677 -12052.5
## - MIA             1      10.9 17677 -12051.3
## - MINN            1      11.0 17677 -12051.2
## - SD              1      11.5 17678 -12050.4
## - OAK             1      11.6 17678 -12050.3
## - NYG             1      12.2 17679 -12049.3
## - DET             1      13.5 17680 -12047.4
## - ARI             1      13.5 17680 -12047.3
## - CHI             1      14.1 17681 -12046.3
## - PHI             1      14.7 17681 -12045.4
## - BAL             1      16.4 17683 -12042.7
## - WAS             1      17.2 17684 -12041.6
## - ATL             1      18.2 17685 -12040.0
## - HOU             1      19.7 17686 -12037.7
## - PIT             1      23.8 17690 -12031.4
## - avg_rbry_plyr   1      29.5 17696 -12022.5
## - forty1          1      30.6 17697 -12020.7
## - CLE             1      31.4 17698 -12019.5
## - avg_qbtdp_plyr  1      40.9 17707 -12004.8
## - avg_rbry_pos    1      60.6 17727 -11974.2
## - weight          1      76.3 17743 -11949.8
## - avg_rectd_plyr  1    5004.1 22671  -5213.8
## 
## Step:  AIC=-12066.69
## recy ~ weight + cold_weather + forty1 + ARI + ATL + BAL + BUF + 
##     CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU + IND + JAC + 
##     KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + 
##     SD + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## <none>                        17667 -12067
## - BUF             1       2.3 17670 -12065
## - bad_weather_1   1       2.4 17670 -12065
## - DEN             1       2.6 17670 -12065
## - NOR             1       4.0 17671 -12062
## - NYJ             1       4.1 17672 -12062
## - DAL             1       4.2 17672 -12062
## - grass_1         1       4.7 17672 -12061
## - JAC             1       6.1 17674 -12059
## - NE              1       6.4 17674 -12059
## - cold_weather    1       8.0 17675 -12056
## - TEN             1       8.2 17676 -12056
## - TB              1       8.3 17676 -12056
## - IND             1       9.0 17676 -12055
## - KC              1      10.0 17677 -12053
## - STL             1      10.0 17677 -12053
## - CIN             1      10.2 17678 -12053
## - CAR             1      10.3 17678 -12053
## - MINN            1      11.1 17679 -12052
## - MIA             1      11.1 17679 -12052
## - SD              1      11.3 17679 -12051
## - OAK             1      11.8 17679 -12050
## - NYG             1      12.3 17680 -12050
## - DET             1      13.6 17681 -12048
## - ARI             1      13.6 17681 -12048
## - CHI             1      14.3 17682 -12046
## - PHI             1      14.9 17682 -12046
## - BAL             1      16.5 17684 -12043
## - WAS             1      17.4 17685 -12042
## - ATL             1      18.3 17686 -12040
## - HOU             1      19.8 17687 -12038
## - PIT             1      23.7 17691 -12032
## - avg_rbry_plyr   1      29.4 17697 -12023
## - forty1          1      30.6 17698 -12021
## - CLE             1      31.6 17699 -12020
## - avg_qbtdp_plyr  1      40.9 17708 -12005
## - avg_rbry_pos    1      60.5 17728 -11975
## - weight          1      76.2 17744 -11950
## - avg_rectd_plyr  1    5004.5 22672  -5214

AIC appeared to be very similar to linear regression

Receptions

Preprocess:

set.seed(123)
splitrec <- sample.split(nfl_data$rec, SplitRatio = 0.7)
TrainRec <- subset(nfl_data, split == TRUE)
TestRec <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(TrainRec, method = c("center", "scale"))
trainTransformedrec <- predict(preProcValues, TrainRec)
testTransformedrec <- predict(preProcValues, TestRec)

ggpairs:

ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("rec",colnames(filtered_nfl_data_fields[46:51]))])

####Regressions

recregform <- formula(paste("rec ~ ", 
                               paste(colnames(filtered_nfl_data_fields), collapse="+")))



linRegrec <- lm(recregform, data = trainTransformedrec)
summary(linRegrec)
## 
## Call:
## lm(formula = recregform, data = trainTransformedrec)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3983 -0.5040 -0.1305  0.3285  6.4639 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -4.263e-15  4.892e-03   0.000 1.000000    
## height          -5.461e-02  9.491e-03  -5.754 8.80e-09 ***
## weight          -2.440e-02  8.895e-03  -2.743 0.006086 ** 
## cold_weather    -1.923e-02  5.149e-03  -3.735 0.000188 ***
## hot_weather     -6.469e-03  4.937e-03  -1.310 0.190046    
## home_team_1     -1.158e-02  5.323e-03  -2.176 0.029552 *  
## forty1          -1.172e-02  8.442e-03  -1.388 0.165044    
## vertical1       -8.435e-03  6.491e-03  -1.299 0.193796    
## ARI              3.153e-02  6.843e-03   4.608 4.08e-06 ***
## ATL              4.264e-02  6.876e-03   6.201 5.69e-10 ***
## BAL              4.300e-02  6.882e-03   6.248 4.21e-10 ***
## BUF              2.455e-02  6.793e-03   3.614 0.000302 ***
## CAR              2.053e-02  6.749e-03   3.042 0.002349 ** 
## CHI              3.920e-02  6.673e-03   5.874 4.30e-09 ***
## CIN              3.801e-02  6.796e-03   5.593 2.26e-08 ***
## CLE              5.026e-02  6.765e-03   7.429 1.13e-13 ***
## DAL              2.544e-02  6.834e-03   3.722 0.000198 ***
## DEN              2.065e-02  6.860e-03   3.011 0.002610 ** 
## DET              4.279e-02  6.765e-03   6.325 2.57e-10 ***
## GB               1.068e-02  6.965e-03   1.533 0.125309    
## HOU              4.230e-02  6.882e-03   6.147 8.02e-10 ***
## IND              3.629e-02  6.832e-03   5.312 1.10e-07 ***
## JAC              3.418e-02  6.664e-03   5.129 2.93e-07 ***
## KC               3.732e-02  6.810e-03   5.480 4.29e-08 ***
## MIA              3.389e-02  6.700e-03   5.058 4.27e-07 ***
## MINN             4.262e-02  6.741e-03   6.323 2.61e-10 ***
## NE               2.320e-02  7.041e-03   3.295 0.000987 ***
## NOR              3.709e-02  7.019e-03   5.284 1.28e-07 ***
## NYG              3.193e-02  6.861e-03   4.655 3.26e-06 ***
## NYJ              2.036e-02  6.835e-03   2.979 0.002899 ** 
## OAK              3.707e-02  6.878e-03   5.389 7.15e-08 ***
## PHI              3.422e-02  6.665e-03   5.135 2.85e-07 ***
## PIT              4.368e-02  6.840e-03   6.385 1.74e-10 ***
## SD               3.523e-02  6.712e-03   5.248 1.55e-07 ***
## SEA              5.694e-03  6.966e-03   0.817 0.413725    
## STL              3.416e-02  6.780e-03   5.038 4.73e-07 ***
## TB               2.219e-02  6.717e-03   3.303 0.000957 ***
## TEN              2.769e-02  6.757e-03   4.097 4.20e-05 ***
## WAS              3.684e-02  6.793e-03   5.424 5.89e-08 ***
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr   5.405e-01  6.247e-03  86.520  < 2e-16 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr    1.298e-01  7.476e-03  17.365  < 2e-16 ***
## avg_rbry_pos    -7.565e-02  8.711e-03  -8.685  < 2e-16 ***
## avg_fuml_plyr   -6.774e-03  7.226e-03  -0.937 0.348541    
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -9.907e-02  7.849e-03 -12.621  < 2e-16 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -1.219e-02  5.628e-03  -2.166 0.030352 *  
## bad_weather_1   -1.059e-02  4.976e-03  -2.127 0.033423 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.811 on 27438 degrees of freedom
## Multiple R-squared:  0.3434, Adjusted R-squared:  0.3423 
## F-statistic: 318.8 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegrec2 <- update(linRegrec, ~. -hot_weather -forty1 -GB - SEA -avg_trg_team -avg_tdr_team
                     -avg_rbra_team -avg_fuml_team -avg_qbtdp_team - avg_qbints_team)
summary(linRegrec2)
## 
## Call:
## lm(formula = rec ~ height + weight + cold_weather + home_team_1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1, data = trainTransformedrec)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4209 -0.5034 -0.1309  0.3328  6.4705 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -4.117e-15  4.892e-03   0.000 1.000000    
## height         -5.471e-02  9.491e-03  -5.764 8.30e-09 ***
## weight         -2.930e-02  8.141e-03  -3.599 0.000320 ***
## cold_weather   -1.831e-02  5.123e-03  -3.575 0.000351 ***
## home_team_1    -1.155e-02  5.322e-03  -2.171 0.029960 *  
## vertical1      -4.085e-03  5.539e-03  -0.737 0.460839    
## ARI             2.666e-02  5.614e-03   4.749 2.05e-06 ***
## ATL             3.730e-02  5.633e-03   6.623 3.59e-11 ***
## BAL             3.765e-02  5.566e-03   6.765 1.36e-11 ***
## BUF             1.944e-02  5.550e-03   3.503 0.000460 ***
## CAR             1.562e-02  5.537e-03   2.820 0.004799 ** 
## CHI             3.435e-02  5.517e-03   6.226 4.85e-10 ***
## CIN             3.262e-02  5.545e-03   5.883 4.07e-09 ***
## CLE             4.498e-02  5.565e-03   8.084 6.53e-16 ***
## DAL             2.017e-02  5.601e-03   3.601 0.000317 ***
## DEN             1.502e-02  5.578e-03   2.693 0.007076 ** 
## DET             3.750e-02  5.571e-03   6.733 1.70e-11 ***
## HOU             3.675e-02  5.638e-03   6.517 7.28e-11 ***
## IND             3.111e-02  5.584e-03   5.571 2.56e-08 ***
## JAC             2.900e-02  5.522e-03   5.251 1.52e-07 ***
## KC              3.215e-02  5.575e-03   5.767 8.16e-09 ***
## MIA             2.886e-02  5.521e-03   5.227 1.73e-07 ***
## MINN            3.747e-02  5.549e-03   6.752 1.49e-11 ***
## NE              1.674e-02  5.633e-03   2.971 0.002969 ** 
## NOR             3.146e-02  5.652e-03   5.566 2.64e-08 ***
## NYG             2.637e-02  5.564e-03   4.741 2.14e-06 ***
## NYJ             1.466e-02  5.568e-03   2.632 0.008481 ** 
## OAK             3.227e-02  5.625e-03   5.737 9.74e-09 ***
## PHI             2.928e-02  5.505e-03   5.319 1.05e-07 ***
## PIT             3.819e-02  5.564e-03   6.863 6.89e-12 ***
## SD              2.956e-02  5.545e-03   5.331 9.86e-08 ***
## STL             2.873e-02  5.595e-03   5.135 2.85e-07 ***
## TB              1.688e-02  5.539e-03   3.048 0.002303 ** 
## TEN             2.255e-02  5.564e-03   4.052 5.08e-05 ***
## WAS             3.198e-02  5.557e-03   5.755 8.73e-09 ***
## avg_rectd_plyr  5.423e-01  6.172e-03  87.875  < 2e-16 ***
## avg_rbry_plyr   1.315e-01  7.367e-03  17.849  < 2e-16 ***
## avg_rbry_pos   -7.500e-02  8.704e-03  -8.617  < 2e-16 ***
## avg_fuml_plyr  -7.142e-03  7.223e-03  -0.989 0.322784    
## avg_qbtdp_plyr -1.016e-01  7.524e-03 -13.506  < 2e-16 ***
## grass_1        -1.263e-02  5.550e-03  -2.275 0.022914 *  
## bad_weather_1  -1.047e-02  4.976e-03  -2.104 0.035390 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.811 on 27442 degrees of freedom
## Multiple R-squared:  0.3432, Adjusted R-squared:  0.3422 
## F-statistic: 349.8 on 41 and 27442 DF,  p-value: < 2.2e-16

We had a modest r-square improvement. The R2 is not very strong (0.4457), and we achieved approximately the same value when we cut the variables down to just 6. Much simpler model with similar results

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

RecPredicted <- predict(linRegrec2, newdata = testTransformedrec)

SSErec <- sum((RecPredicted - testTransformedrec$rec)^2)
SSTrec <- sum((mean(nfl_data$rec)-testTransformedrec$rec)^2)
r2_rec <- 1 - SSErec/SSTrec 
r2_rec
## [1] 0.8782749
rmse_rec <- sqrt(SSErec/nrow(testTransformedrec))
rmse_rec
## [1] 0.7969974

Looking at the regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegrec2, which = c(1,2,3,5))

The charts show very similarly to what we saw above for receiving yards.

The summary statistics are below:

confint(linRegrec2)
##                       2.5 %        97.5 %
## (Intercept)    -0.009588716  0.0095887159
## height         -0.073311748 -0.0361050567
## weight         -0.045255501 -0.0133437044
## cold_weather   -0.028355199 -0.0082735662
## home_team_1    -0.021982346 -0.0011211872
## vertical1      -0.014940648  0.0067714074
## ARI             0.015659421  0.0376682885
## ATL             0.026264525  0.0483453015
## BAL             0.026742150  0.0485595637
## BUF             0.008565760  0.0303229949
## CAR             0.004764205  0.0264702673
## CHI             0.023535464  0.0451622569
## CIN             0.021751469  0.0434865873
## CLE             0.034077046  0.0558912642
## DAL             0.009192547  0.0311496124
## DEN             0.004090978  0.0259579177
## DET             0.026585238  0.0484223772
## HOU             0.025694103  0.0477960158
## IND             0.020163375  0.0420543502
## JAC             0.018173687  0.0398186007
## KC              0.021223060  0.0430769410
## MIA             0.018036876  0.0396783173
## MINN            0.026591036  0.0483440036
## NE              0.005695593  0.0277778225
## NOR             0.020379366  0.0425360434
## NYG             0.015470120  0.0372797756
## NYJ             0.003744224  0.0255720611
## OAK             0.021246695  0.0432984222
## PHI             0.018488304  0.0400684540
## PIT             0.027280183  0.0490917161
## SD              0.018690394  0.0404276600
## STL             0.017761430  0.0396942051
## TB              0.006028188  0.0277415125
## TEN             0.011642942  0.0334557042
## WAS             0.021089472  0.0428718167
## avg_rectd_plyr  0.530241430  0.5544352471
## avg_rbry_plyr   0.117052640  0.1459311941
## avg_rbry_pos   -0.092064124 -0.0579440215
## avg_fuml_plyr  -0.021300372  0.0070158912
## avg_qbtdp_plyr -0.116366581 -0.0868717574
## grass_1        -0.023503224 -0.0017478469
## bad_weather_1  -0.020222651 -0.0007161738
coef(summary(linRegrec2))
##                     Estimate  Std. Error       t value     Pr(>|t|)
## (Intercept)    -4.117011e-15 0.004892076 -8.415672e-13 1.000000e+00
## height         -5.470840e-02 0.009491259 -5.764083e+00 8.298176e-09
## weight         -2.929960e-02 0.008140555 -3.599214e+00 3.197418e-04
## cold_weather   -1.831438e-02 0.005122734 -3.575119e+00 3.506695e-04
## home_team_1    -1.155177e-02 0.005321587 -2.170737e+00 2.995960e-02
## vertical1      -4.084620e-03 0.005538647 -7.374762e-01 4.608391e-01
## ARI             2.666385e-02 0.005614363  4.749222e+00 2.052317e-06
## ATL             3.730491e-02 0.005632706  6.622911e+00 3.586973e-11
## BAL             3.765086e-02 0.005565523  6.765016e+00 1.359713e-11
## BUF             1.944438e-02 0.005550172  3.503383e+00 4.601199e-04
## CAR             1.561724e-02 0.005537118  2.820463e+00 4.798883e-03
## CHI             3.434886e-02 0.005516897  6.226120e+00 4.850519e-10
## CIN             3.261903e-02 0.005544530  5.883100e+00 4.073201e-09
## CLE             4.498416e-02 0.005564708  8.083830e+00 6.532687e-16
## DAL             2.017108e-02 0.005601148  3.601240e+00 3.172614e-04
## DEN             1.502445e-02 0.005578157  2.693443e+00 7.076126e-03
## DET             3.750381e-02 0.005570555  6.732508e+00 1.700495e-11
## HOU             3.674506e-02 0.005638098  6.517279e+00 7.283502e-11
## IND             3.110886e-02 0.005584289  5.570783e+00 2.559725e-08
## JAC             2.899614e-02 0.005521520  5.251479e+00 1.520063e-07
## KC              3.215000e-02 0.005574826  5.766996e+00 8.156229e-09
## MIA             2.885760e-02 0.005520634  5.227225e+00 1.733312e-07
## MINN            3.746752e-02 0.005549084  6.752019e+00 1.487078e-11
## NE              1.673671e-02 0.005633077  2.971149e+00 2.969453e-03
## NOR             3.145770e-02 0.005652068  5.565698e+00 2.635426e-08
## NYG             2.637495e-02 0.005563544  4.740674e+00 2.140769e-06
## NYJ             1.465814e-02 0.005568182  2.632482e+00 8.481086e-03
## OAK             3.227256e-02 0.005625296  5.737042e+00 9.735669e-09
## PHI             2.927838e-02 0.005504999  5.318508e+00 1.054402e-07
## PIT             3.818595e-02 0.005564024  6.863010e+00 6.885796e-12
## SD              2.955903e-02 0.005545078  5.330678e+00 9.861900e-08
## STL             2.872782e-02 0.005594952  5.134596e+00 2.846801e-07
## TB              1.688485e-02 0.005538971  3.048373e+00 2.303029e-03
## TEN             2.254932e-02 0.005564337  4.052473e+00 5.081867e-05
## WAS             3.198064e-02 0.005556578  5.755457e+00 8.732710e-09
## avg_rectd_plyr  5.423383e-01 0.006171733  8.787456e+01 0.000000e+00
## avg_rbry_plyr   1.314919e-01 0.007366788  1.784929e+01 7.370893e-71
## avg_rbry_pos   -7.500407e-02 0.008703884 -8.617311e+00 7.216658e-18
## avg_fuml_plyr  -7.142240e-03 0.007223351 -9.887711e-01 3.227839e-01
## avg_qbtdp_plyr -1.016192e-01 0.007523996 -1.350601e+01 1.955406e-41
## grass_1        -1.262554e-02 0.005549698 -2.274995e+00 2.291391e-02
## bad_weather_1  -1.046941e-02 0.004976014 -2.103976e+00 3.538965e-02
anova(linRegrec2)
## Analysis of Variance Table
## 
## Response: rec
##                   Df  Sum Sq Mean Sq    F value    Pr(>F)    
## height             1     0.2     0.2     0.3588 0.5491700    
## weight             1   326.5   326.5   496.4268 < 2.2e-16 ***
## cold_weather       1    20.0    20.0    30.4066 3.535e-08 ***
## home_team_1        1    12.3    12.3    18.7076 1.529e-05 ***
## vertical1          1   748.4   748.4  1137.8367 < 2.2e-16 ***
## ARI                1     3.5     3.5     5.2794 0.0215870 *  
## ATL                1    36.6    36.6    55.6655 8.846e-14 ***
## BAL                1     0.6     0.6     0.9800 0.3222059    
## BUF                1     2.2     2.2     3.3080 0.0689538 .  
## CAR                1     8.1     8.1    12.3639 0.0004384 ***
## CHI                1     0.5     0.5     0.8096 0.3682460    
## CIN                1     0.2     0.2     0.3079 0.5789480    
## CLE                1     3.9     3.9     5.9089 0.0150710 *  
## DAL                1     4.1     4.1     6.2492 0.0124309 *  
## DEN                1     0.3     0.3     0.3959 0.5292150    
## DET                1    12.9    12.9    19.6460 9.356e-06 ***
## HOU                1     0.1     0.1     0.0928 0.7606060    
## IND                1     2.3     2.3     3.4616 0.0628218 .  
## JAC                1     3.2     3.2     4.9407 0.0262397 *  
## KC                 1     4.3     4.3     6.4946 0.0108256 *  
## MIA                1     1.2     1.2     1.7795 0.1822205    
## MINN               1     6.7     6.7    10.1983 0.0014073 ** 
## NE                 1    47.7    47.7    72.5198 < 2.2e-16 ***
## NOR                1    32.1    32.1    48.7564 2.964e-12 ***
## NYG                1     6.3     6.3     9.5470 0.0020048 ** 
## NYJ                1    13.5    13.5    20.4518 6.141e-06 ***
## OAK                1     3.6     3.6     5.4105 0.0200235 *  
## PHI                1     7.7     7.7    11.7561 0.0006073 ***
## PIT                1    18.4    18.4    27.9729 1.240e-07 ***
## SD                 1    13.8    13.8    21.0393 4.520e-06 ***
## STL                1     0.0     0.0     0.0049 0.9444320    
## TB                 1     0.1     0.1     0.1522 0.6964744    
## TEN                1     5.5     5.5     8.2967 0.0039749 ** 
## WAS                1     1.6     1.6     2.4295 0.1190812    
## avg_rectd_plyr     1  7645.2  7645.2 11623.1297 < 2.2e-16 ***
## avg_rbry_plyr      1   159.2   159.2   242.0776 < 2.2e-16 ***
## avg_rbry_pos       1    62.5    62.5    95.0615 < 2.2e-16 ***
## avg_fuml_plyr      1    90.7    90.7   137.8181 < 2.2e-16 ***
## avg_qbtdp_plyr     1   120.3   120.3   182.8737 < 2.2e-16 ***
## grass_1            1     3.6     3.6     5.4809 0.0192327 *  
## bad_weather_1      1     2.9     2.9     4.4267 0.0353896 *  
## Residuals      27442 18050.2     0.7                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Like the model above, linear regression may not be the best predictor for this statistic

AIC:

aic_rec <- step(lm(recregform, data = TrainRecy), direction = "backward")
## Start:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=34192.2
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## - SEA             1       2.3  95046 34191
## - avg_fuml_plyr   1       3.0  95046 34191
## - vertical1       1       5.8  95049 34192
## - hot_weather     1       5.9  95049 34192
## - forty1          1       6.7  95050 34192
## <none>                         95043 34192
## - GB              1       8.1  95052 34193
## - bad_weather_1   1      15.7  95059 34195
## - grass_1         1      16.2  95060 34195
## - home_team_1     1      16.4  95060 34195
## - weight          1      26.1  95069 34198
## - NYJ             1      30.7  95074 34199
## - DEN             1      31.4  95075 34199
## - CAR             1      32.1  95075 34199
## - NE              1      37.6  95081 34201
## - TB              1      37.8  95081 34201
## - BUF             1      45.2  95089 34203
## - DAL             1      48.0  95091 34204
## - cold_weather    1      48.3  95092 34204
## - TEN             1      58.1  95102 34207
## - ARI             1      73.6  95117 34211
## - NYG             1      75.0  95118 34212
## - STL             1      87.9  95131 34216
## - MIA             1      88.6  95132 34216
## - JAC             1      91.1  95135 34217
## - PHI             1      91.3  95135 34217
## - SD              1      95.4  95139 34218
## - NOR             1      96.7  95140 34218
## - IND             1      97.7  95141 34218
## - OAK             1     100.6  95144 34219
## - WAS             1     101.9  95145 34220
## - KC              1     104.0  95147 34220
## - CIN             1     108.3  95152 34222
## - height          1     114.7  95158 34223
## - CHI             1     119.5  95163 34225
## - HOU             1     130.9  95174 34228
## - ATL             1     133.2  95177 34229
## - BAL             1     135.2  95179 34229
## - MINN            1     138.5  95182 34230
## - DET             1     138.6  95182 34230
## - PIT             1     141.2  95185 34231
## - CLE             1     191.2  95235 34245
## - avg_rbry_pos    1     261.3  95305 34266
## - avg_qbtdp_plyr  1     551.8  95595 34349
## - avg_rbry_plyr   1    1044.5  96088 34491
## - avg_rectd_plyr  1   25930.1 120973 40820
## 
## Step:  AIC=34190.87
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## - avg_fuml_plyr   1       3.2  95049 34190
## - hot_weather     1       5.6  95051 34190
## - GB              1       5.8  95052 34191
## - vertical1       1       5.9  95052 34191
## - forty1          1       6.8  95052 34191
## <none>                         95046 34191
## - bad_weather_1   1      15.7  95061 34193
## - home_team_1     1      16.2  95062 34194
## - grass_1         1      18.2  95064 34194
## - weight          1      26.1  95072 34196
## - NYJ             1      30.7  95076 34198
## - DEN             1      31.3  95077 34198
## - CAR             1      31.9  95078 34198
## - TB              1      38.4  95084 34200
## - NE              1      39.0  95085 34200
## - cold_weather    1      47.0  95093 34202
## - BUF             1      47.7  95093 34203
## - DAL             1      50.7  95096 34204
## - TEN             1      62.3  95108 34207
## - ARI             1      81.5  95127 34212
## - NYG             1      84.1  95130 34213
## - STL             1      98.5  95144 34217
## - MIA             1      98.7  95144 34217
## - JAC             1     101.3  95147 34218
## - PHI             1     101.8  95147 34218
## - SD              1     106.3  95152 34220
## - IND             1     111.6  95157 34221
## - NOR             1     111.8  95157 34221
## - OAK             1     113.8  95159 34222
## - height          1     114.9  95161 34222
## - WAS             1     115.7  95161 34222
## - KC              1     118.1  95164 34223
## - CIN             1     125.0  95171 34225
## - CHI             1     135.8  95182 34228
## - HOU             1     152.2  95198 34233
## - ATL             1     154.9  95201 34234
## - BAL             1     159.7  95205 34235
## - DET             1     160.9  95207 34235
## - MINN            1     161.4  95207 34236
## - PIT             1     165.0  95211 34237
## - CLE             1     225.4  95271 34254
## - avg_rbry_pos    1     261.6  95307 34264
## - avg_qbtdp_plyr  1     550.2  95596 34347
## - avg_rbry_plyr   1    1045.6  96091 34490
## - avg_rectd_plyr  1   25931.2 120977 40819
## 
## Step:  AIC=34189.79
## rec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## - hot_weather     1       5.6  95054 34189
## - vertical1       1       5.8  95055 34189
## - GB              1       5.9  95055 34190
## - forty1          1       6.9  95056 34190
## <none>                         95049 34190
## - bad_weather_1   1      15.6  95064 34192
## - home_team_1     1      16.3  95065 34193
## - grass_1         1      18.1  95067 34193
## - weight          1      24.7  95074 34195
## - NYJ             1      29.8  95079 34196
## - DEN             1      30.6  95079 34197
## - CAR             1      31.4  95080 34197
## - TB              1      37.6  95086 34199
## - NE              1      40.0  95089 34199
## - cold_weather    1      46.7  95096 34201
## - BUF             1      46.9  95096 34201
## - DAL             1      50.4  95099 34202
## - TEN             1      61.2  95110 34205
## - ARI             1      80.4  95129 34211
## - NYG             1      83.3  95132 34212
## - STL             1      97.3  95146 34216
## - MIA             1      97.6  95147 34216
## - PHI             1     100.0  95149 34217
## - JAC             1     100.8  95150 34217
## - SD              1     105.5  95154 34218
## - IND             1     110.9  95160 34220
## - NOR             1     112.2  95161 34220
## - OAK             1     113.6  95162 34221
## - WAS             1     114.1  95163 34221
## - height          1     117.2  95166 34222
## - KC              1     117.3  95166 34222
## - CIN             1     124.3  95173 34224
## - CHI             1     134.1  95183 34227
## - HOU             1     152.1  95201 34232
## - ATL             1     155.7  95205 34233
## - DET             1     159.4  95208 34234
## - BAL             1     159.5  95208 34234
## - MINN            1     160.6  95209 34234
## - PIT             1     163.5  95212 34235
## - CLE             1     223.1  95272 34252
## - avg_rbry_pos    1     262.8  95312 34264
## - avg_qbtdp_plyr  1     913.6  95962 34451
## - avg_rbry_plyr   1    1132.3  96181 34513
## - avg_rectd_plyr  1   25934.9 120984 40819
## 
## Step:  AIC=34189.41
## rec ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## - vertical1       1       5.8  95060 34189
## - GB              1       6.2  95061 34189
## <none>                         95054 34189
## - forty1          1       6.9  95061 34189
## - bad_weather_1   1      15.4  95070 34192
## - home_team_1     1      16.2  95071 34192
## - grass_1         1      19.6  95074 34193
## - weight          1      24.4  95079 34194
## - NYJ             1      29.4  95084 34196
## - DEN             1      31.0  95085 34196
## - CAR             1      32.2  95087 34197
## - TB              1      37.3  95092 34198
## - NE              1      40.5  95095 34199
## - cold_weather    1      45.7  95100 34201
## - BUF             1      46.5  95101 34201
## - DAL             1      51.1  95106 34202
## - TEN             1      62.3  95117 34205
## - ARI             1      81.3  95136 34211
## - NYG             1      84.0  95138 34212
## - STL             1      96.8  95151 34215
## - MIA             1      99.0  95153 34216
## - PHI             1     101.3  95156 34217
## - JAC             1     102.3  95157 34217
## - SD              1     104.5  95159 34218
## - IND             1     111.8  95166 34220
## - NOR             1     112.2  95167 34220
## - OAK             1     115.3  95170 34221
## - WAS             1     115.6  95170 34221
## - height          1     117.5  95172 34221
## - KC              1     118.9  95173 34222
## - CIN             1     125.3  95180 34224
## - CHI             1     135.6  95190 34227
## - HOU             1     153.4  95208 34232
## - ATL             1     157.0  95212 34233
## - DET             1     160.7  95215 34234
## - BAL             1     160.7  95215 34234
## - MINN            1     161.8  95216 34234
## - PIT             1     163.9  95218 34235
## - CLE             1     225.1  95280 34252
## - avg_rbry_pos    1     262.5  95317 34263
## - avg_qbtdp_plyr  1     913.0  95967 34450
## - avg_rbry_plyr   1    1131.0  96185 34513
## - avg_rectd_plyr  1   25935.9 120990 40818
## 
## Step:  AIC=34189.08
## rec ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + 
##     NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## - forty1          1       2.6  95063 34188
## - GB              1       6.7  95067 34189
## <none>                         95060 34189
## - bad_weather_1   1      15.5  95076 34192
## - home_team_1     1      16.2  95076 34192
## - grass_1         1      19.5  95080 34193
## - weight          1      26.3  95086 34195
## - NYJ             1      28.5  95089 34195
## - DEN             1      30.3  95091 34196
## - CAR             1      32.2  95092 34196
## - TB              1      38.1  95098 34198
## - NE              1      41.1  95101 34199
## - cold_weather    1      45.8  95106 34200
## - BUF             1      48.2  95108 34201
## - DAL             1      51.6  95112 34202
## - TEN             1      62.1  95122 34205
## - ARI             1      82.8  95143 34211
## - NYG             1      84.8  95145 34212
## - STL             1      98.8  95159 34216
## - JAC             1     100.2  95160 34216
## - MIA             1     100.9  95161 34216
## - PHI             1     103.1  95163 34217
## - SD              1     105.6  95166 34218
## - IND             1     111.2  95171 34219
## - NOR             1     112.6  95173 34220
## - WAS             1     116.2  95176 34221
## - OAK             1     117.6  95178 34221
## - height          1     118.8  95179 34221
## - KC              1     119.6  95180 34222
## - CIN             1     126.4  95187 34224
## - CHI             1     138.1  95198 34227
## - HOU             1     152.5  95213 34231
## - DET             1     159.2  95219 34233
## - MINN            1     160.4  95221 34233
## - ATL             1     160.7  95221 34234
## - BAL             1     161.7  95222 34234
## - PIT             1     164.8  95225 34235
## - CLE             1     223.7  95284 34252
## - avg_rbry_pos    1     261.0  95321 34262
## - avg_qbtdp_plyr  1     909.6  95970 34449
## - avg_rbry_plyr   1    1145.3  96206 34516
## - avg_rectd_plyr  1   25958.6 121019 40823
## 
## Step:  AIC=34187.84
## rec ~ height + weight + cold_weather + home_team_1 + ARI + ATL + 
##     BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## - GB              1       6.4  95069 34188
## <none>                         95063 34188
## - bad_weather_1   1      15.5  95078 34190
## - home_team_1     1      16.2  95079 34191
## - grass_1         1      19.5  95082 34191
## - NYJ             1      28.2  95091 34194
## - DEN             1      30.0  95093 34195
## - CAR             1      32.6  95096 34195
## - TB              1      37.8  95101 34197
## - NE              1      39.1  95102 34197
## - weight          1      41.6  95104 34198
## - cold_weather    1      45.8  95109 34199
## - BUF             1      48.4  95111 34200
## - DAL             1      51.1  95114 34201
## - TEN             1      61.8  95125 34204
## - ARI             1      83.3  95146 34210
## - NYG             1      83.6  95147 34210
## - STL             1      97.4  95160 34214
## - JAC             1      99.8  95163 34215
## - MIA             1     100.1  95163 34215
## - PHI             1     102.5  95165 34215
## - SD              1     104.1  95167 34216
## - IND             1     111.5  95174 34218
## - NOR             1     112.5  95175 34218
## - WAS             1     117.4  95180 34220
## - height          1     118.3  95181 34220
## - OAK             1     118.8  95182 34220
## - KC              1     119.3  95182 34220
## - CIN             1     125.1  95188 34222
## - CHI             1     137.7  95201 34226
## - HOU             1     151.0  95214 34229
## - DET             1     158.5  95221 34232
## - ATL             1     159.0  95222 34232
## - MINN            1     160.1  95223 34232
## - BAL             1     161.3  95224 34232
## - PIT             1     164.1  95227 34233
## - CLE             1     222.9  95286 34250
## - avg_rbry_pos    1     260.4  95323 34261
## - avg_qbtdp_plyr  1    1172.9  96236 34523
## - avg_rbry_plyr   1    1198.2  96261 34530
## - avg_rectd_plyr  1   26926.6 121990 41040
## 
## Step:  AIC=34187.7
## rec ~ height + weight + cold_weather + home_team_1 + ARI + ATL + 
##     BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + HOU + 
##     IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq    RSS   AIC
## <none>                         95069 34188
## - bad_weather_1   1      15.3  95085 34190
## - home_team_1     1      16.5  95086 34190
## - grass_1         1      17.8  95087 34191
## - NYJ             1      22.5  95092 34192
## - DEN             1      24.1  95093 34193
## - CAR             1      26.7  95096 34193
## - TB              1      31.7  95101 34195
## - NE              1      32.8  95102 34195
## - weight          1      41.2  95110 34198
## - BUF             1      42.1  95111 34198
## - cold_weather    1      44.0  95113 34198
## - DAL             1      44.7  95114 34199
## - TEN             1      55.3  95125 34202
## - ARI             1      77.0  95146 34208
## - NYG             1      77.5  95147 34208
## - STL             1      91.3  95161 34212
## - JAC             1      93.9  95163 34213
## - MIA             1      94.3  95164 34213
## - PHI             1      96.7  95166 34214
## - SD              1      98.4  95168 34214
## - IND             1     105.9  95175 34216
## - NOR             1     107.4  95177 34217
## - WAS             1     112.3  95182 34218
## - OAK             1     113.8  95183 34219
## - KC              1     114.3  95184 34219
## - height          1     118.4  95188 34220
## - CIN             1     119.9  95189 34220
## - CHI             1     133.1  95202 34224
## - HOU             1     146.7  95216 34228
## - DET             1     154.5  95224 34230
## - ATL             1     155.2  95224 34231
## - MINN            1     156.0  95225 34231
## - BAL             1     158.2  95227 34231
## - PIT             1     161.6  95231 34232
## - CLE             1     222.9  95292 34250
## - avg_rbry_pos    1     257.9  95327 34260
## - avg_qbtdp_plyr  1    1167.3  96237 34521
## - avg_rbry_plyr   1    1195.7  96265 34529
## - avg_rectd_plyr  1   27169.4 122239 41094

AIC appeared to be very similar to the linear regression

Targets

Preprocess:

set.seed(123)
splittrg <- sample.split(nfl_data$trg, SplitRatio = 0.7)
Traintrg <- subset(nfl_data, split == TRUE)
Testtrg <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Traintrg, method = c("center", "scale"))
trainTransformedtrg <- predict(preProcValues, Traintrg)
testTransformedtrg <- predict(preProcValues, Testtrg)

ggpairs:

ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("trg",colnames(filtered_nfl_data_fields[46:51]))])

trgregform <- formula(paste("trg ~ ", 
                            paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegtrg <- lm(trgregform, data = trainTransformedtrg)

summary(linRegtrg)
## 
## Call:
## lm(formula = trgregform, data = trainTransformedtrg)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.7736 -0.4601 -0.1111  0.3197  5.3233 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -1.716e-15  4.567e-03   0.000 1.000000    
## height          -1.979e-02  8.861e-03  -2.234 0.025511 *  
## weight          -6.511e-02  8.305e-03  -7.840 4.68e-15 ***
## cold_weather    -7.148e-03  4.808e-03  -1.487 0.137097    
## hot_weather     -5.357e-03  4.609e-03  -1.162 0.245100    
## home_team_1     -1.690e-02  4.969e-03  -3.402 0.000671 ***
## forty1          -4.129e-02  7.882e-03  -5.238 1.63e-07 ***
## vertical1        6.284e-04  6.060e-03   0.104 0.917408    
## ARI              3.596e-02  6.389e-03   5.629 1.83e-08 ***
## ATL              2.773e-02  6.419e-03   4.320 1.57e-05 ***
## BAL              3.933e-02  6.425e-03   6.121 9.43e-10 ***
## BUF              2.473e-02  6.342e-03   3.899 9.67e-05 ***
## CAR              2.227e-02  6.301e-03   3.535 0.000409 ***
## CHI              2.860e-02  6.231e-03   4.591 4.43e-06 ***
## CIN              2.927e-02  6.345e-03   4.612 4.00e-06 ***
## CLE              5.271e-02  6.316e-03   8.345  < 2e-16 ***
## DAL              7.146e-03  6.380e-03   1.120 0.262697    
## DEN              1.239e-02  6.404e-03   1.935 0.053034 .  
## DET              3.610e-02  6.316e-03   5.715 1.11e-08 ***
## GB              -7.034e-03  6.503e-03  -1.082 0.279411    
## HOU              4.004e-02  6.425e-03   6.231 4.69e-10 ***
## IND              3.530e-02  6.378e-03   5.535 3.14e-08 ***
## JAC              3.907e-02  6.222e-03   6.280 3.45e-10 ***
## KC               2.922e-02  6.358e-03   4.595 4.34e-06 ***
## MIA              2.997e-02  6.256e-03   4.790 1.68e-06 ***
## MINN             3.504e-02  6.294e-03   5.568 2.61e-08 ***
## NE               1.349e-02  6.573e-03   2.052 0.040222 *  
## NOR              1.142e-02  6.553e-03   1.742 0.081465 .  
## NYG              2.910e-02  6.405e-03   4.543 5.58e-06 ***
## NYJ              2.792e-02  6.382e-03   4.374 1.22e-05 ***
## OAK              3.254e-02  6.422e-03   5.067 4.07e-07 ***
## PHI              3.026e-02  6.223e-03   4.863 1.16e-06 ***
## PIT              2.865e-02  6.386e-03   4.486 7.29e-06 ***
## SD               2.118e-02  6.267e-03   3.380 0.000726 ***
## SEA             -1.205e-02  6.504e-03  -1.852 0.064026 .  
## STL              3.460e-02  6.330e-03   5.467 4.63e-08 ***
## TB               2.346e-02  6.271e-03   3.741 0.000184 ***
## TEN              2.529e-02  6.309e-03   4.009 6.10e-05 ***
## WAS              2.534e-02  6.342e-03   3.995 6.48e-05 ***
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr   5.746e-01  5.832e-03  98.521  < 2e-16 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr    1.037e-01  6.980e-03  14.855  < 2e-16 ***
## avg_rbry_pos    -1.073e-01  8.133e-03 -13.197  < 2e-16 ***
## avg_fuml_plyr   -2.183e-02  6.747e-03  -3.235 0.001216 ** 
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -8.681e-02  7.328e-03 -11.846  < 2e-16 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -7.245e-03  5.255e-03  -1.379 0.168009    
## bad_weather_1   -6.780e-04  4.646e-03  -0.146 0.883979    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7572 on 27438 degrees of freedom
## Multiple R-squared:  0.4276, Adjusted R-squared:  0.4267 
## F-statistic: 455.5 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegtrg2 <- update(linRegtrg, ~. -height-cold_weather-hot_weather-forty1-vertical1-DAL-DEN-GB-NE-NOR-SEA
                 -avg_trg_team -avg_tdr_team-avg_rbra_team -avg_fuml_team -avg_qbtdp_team 
                 -avg_qbints_team - grass_1-bad_weather_1)

summary(linRegtrg2)
## 
## Call:
## lm(formula = trg ~ weight + home_team_1 + ARI + ATL + BAL + BUF + 
##     CAR + CHI + CIN + CLE + DET + HOU + IND + JAC + KC + MIA + 
##     MINN + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr, data = trainTransformedtrg)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8593 -0.4634 -0.1128  0.3281  5.3615 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -1.617e-15  4.573e-03   0.000 1.000000    
## weight         -1.000e-01  4.631e-03 -21.594  < 2e-16 ***
## home_team_1    -1.995e-02  4.823e-03  -4.137 3.53e-05 ***
## ARI             3.395e-02  4.851e-03   6.998 2.65e-12 ***
## ATL             2.430e-02  4.838e-03   5.023 5.12e-07 ***
## BAL             3.640e-02  4.823e-03   7.547 4.60e-14 ***
## BUF             2.220e-02  4.806e-03   4.620 3.85e-06 ***
## CAR             2.035e-02  4.811e-03   4.230 2.35e-05 ***
## CHI             2.459e-02  4.801e-03   5.121 3.07e-07 ***
## CIN             2.530e-02  4.804e-03   5.267 1.40e-07 ***
## CLE             4.859e-02  4.839e-03  10.040  < 2e-16 ***
## DET             3.359e-02  4.811e-03   6.982 2.97e-12 ***
## HOU             3.599e-02  4.859e-03   7.407 1.33e-13 ***
## IND             3.378e-02  4.822e-03   7.006 2.51e-12 ***
## JAC             3.626e-02  4.795e-03   7.560 4.14e-14 ***
## KC              2.514e-02  4.825e-03   5.211 1.89e-07 ***
## MIA             2.625e-02  4.798e-03   5.471 4.51e-08 ***
## MINN            3.226e-02  4.816e-03   6.699 2.14e-11 ***
## NYG             2.505e-02  4.808e-03   5.209 1.91e-07 ***
## NYJ             2.517e-02  4.822e-03   5.219 1.81e-07 ***
## OAK             2.971e-02  4.823e-03   6.160 7.39e-10 ***
## PHI             2.672e-02  4.802e-03   5.564 2.66e-08 ***
## PIT             2.404e-02  4.811e-03   4.997 5.85e-07 ***
## SD              1.560e-02  4.791e-03   3.257 0.001128 ** 
## STL             3.048e-02  4.848e-03   6.288 3.27e-10 ***
## TB              2.000e-02  4.806e-03   4.161 3.17e-05 ***
## TEN             2.184e-02  4.823e-03   4.527 6.00e-06 ***
## WAS             2.395e-02  4.822e-03   4.966 6.87e-07 ***
## avg_rectd_plyr  5.810e-01  5.664e-03 102.579  < 2e-16 ***
## avg_rbry_plyr   1.091e-01  6.871e-03  15.871  < 2e-16 ***
## avg_rbry_pos   -9.647e-02  7.087e-03 -13.613  < 2e-16 ***
## avg_fuml_plyr  -2.280e-02  6.723e-03  -3.391 0.000696 ***
## avg_qbtdp_plyr -1.057e-01  6.619e-03 -15.977  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.758 on 27451 degrees of freedom
## Multiple R-squared:  0.426,  Adjusted R-squared:  0.4254 
## F-statistic: 636.7 on 32 and 27451 DF,  p-value: < 2.2e-16

Modest gains in second run’s R2. It is a much more simple model, and has a little better descriptive stats.

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

TrgPredicted <- predict(linRegtrg2, newdata = testTransformedtrg)

SSEtrg <- sum((TrgPredicted - testTransformedtrg$trg)^2)
SSTtrg <- sum((mean(nfl_data$trg)-testTransformedtrg$trg)^2)
r2_trg <- 1 - SSEtrg/SSTtrg 
r2_trg
## [1] 0.953245
rmse_trg <- sqrt(SSEtrg/nrow(testTransformedtrg))
rmse_trg
## [1] 0.7421937

The regression plots for targets are below:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegrec2, which = c(1:3,5))

Here are additional summary statistics:

confint(linRegtrg2)
##                       2.5 %       97.5 %
## (Intercept)    -0.008962372  0.008962372
## weight         -0.109072460 -0.090919689
## home_team_1    -0.029407521 -0.010499863
## ARI             0.024443139  0.043461176
## ATL             0.014816272  0.033779985
## BAL             0.026945513  0.045852511
## BUF             0.012784765  0.031622921
## CAR             0.010919267  0.029777561
## CHI             0.015174471  0.033995707
## CIN             0.015884937  0.034717487
## CLE             0.039102914  0.058073333
## DET             0.024163320  0.043024446
## HOU             0.026466108  0.045512540
## IND             0.024332465  0.043237109
## JAC             0.026856263  0.045654833
## KC              0.015685651  0.034600137
## MIA             0.016847793  0.035657765
## MINN            0.022823096  0.041702343
## NYG             0.015622503  0.034469521
## NYJ             0.015717405  0.034621023
## OAK             0.020253373  0.039158780
## PHI             0.017304578  0.036128312
## PIT             0.014610681  0.033468501
## SD              0.006212349  0.024992919
## STL             0.020979488  0.039984055
## TB              0.010580046  0.029420028
## TEN             0.012383540  0.031291995
## WAS             0.014495624  0.033398144
## avg_rectd_plyr  0.569942774  0.592147559
## avg_rbry_plyr   0.095582869  0.122518021
## avg_rbry_pos   -0.110362600 -0.082581821
## avg_fuml_plyr  -0.035976124 -0.009622626
## avg_qbtdp_plyr -0.118718776 -0.092772666
coef(summary(linRegtrg2))
##                     Estimate  Std. Error       t value      Pr(>|t|)
## (Intercept)    -1.616974e-15 0.004572521 -3.536285e-13  1.000000e+00
## weight         -9.999607e-02 0.004630690 -2.159421e+01 1.455031e-102
## home_team_1    -1.995369e-02 0.004823258 -4.136974e+00  3.529640e-05
## ARI             3.395216e-02 0.004851415  6.998403e+00  2.648420e-12
## ATL             2.429813e-02 0.004837557  5.022809e+00  5.124010e-07
## BAL             3.639901e-02 0.004823090  7.546825e+00  4.598244e-14
## BUF             2.220384e-02 0.004805528  4.620479e+00  3.845937e-06
## CAR             2.034841e-02 0.004810665  4.229854e+00  2.346000e-05
## CHI             2.458509e-02 0.004801212  5.120601e+00  3.066202e-07
## CIN             2.530121e-02 0.004804098  5.266589e+00  1.400281e-07
## CLE             4.858812e-02 0.004839268  1.004039e+01  1.112750e-23
## DET             3.359388e-02 0.004811388  6.982160e+00  2.972888e-12
## HOU             3.598932e-02 0.004858659  7.407255e+00  1.326510e-13
## IND             3.378479e-02 0.004822489  7.005674e+00  2.514675e-12
## JAC             3.625555e-02 0.004795430  7.560437e+00  4.142604e-14
## KC              2.514289e-02 0.004825000  5.210963e+00  1.892202e-07
## MIA             2.625278e-02 0.004798339  5.471222e+00  4.508438e-08
## MINN            3.226272e-02 0.004816010  6.699055e+00  2.138233e-11
## NYG             2.504601e-02 0.004807789  5.209465e+00  1.907521e-07
## NYJ             2.516921e-02 0.004822228  5.219416e+00  1.807925e-07
## OAK             2.970608e-02 0.004822684  6.159657e+00  7.391443e-10
## PHI             2.671644e-02 0.004801849  5.563782e+00  2.664494e-08
## PIT             2.403959e-02 0.004810545  4.997270e+00  5.850484e-07
## SD              1.560263e-02 0.004790839  3.256765e+00  1.128265e-03
## STL             3.048177e-02 0.004847979  6.287521e+00  3.274283e-10
## TB              2.000004e-02 0.004805994  4.161478e+00  3.171574e-05
## TEN             2.183777e-02 0.004823461  4.527406e+00  5.996295e-06
## WAS             2.394688e-02 0.004821948  4.966227e+00  6.867755e-07
## avg_rectd_plyr  5.810452e-01 0.005664340  1.025795e+02  0.000000e+00
## avg_rbry_plyr   1.090504e-01 0.006871035  1.587104e+01  1.794185e-56
## avg_rbry_pos   -9.647221e-02 0.007086751 -1.361304e+01  4.589358e-42
## avg_fuml_plyr  -2.279937e-02 0.006722658 -3.391423e+00  6.962880e-04
## avg_qbtdp_plyr -1.057457e-01 0.006618735 -1.597673e+01  3.363564e-57
anova(linRegtrg2)
## Analysis of Variance Table
## 
## Response: trg
##                   Df  Sum Sq Mean Sq    F value    Pr(>F)    
## weight             1   359.6   359.6   625.8500 < 2.2e-16 ***
## home_team_1        1    18.1    18.1    31.4392 2.078e-08 ***
## ARI                1     0.2     0.2     0.3197  0.571799    
## ATL                1     6.1     6.1    10.6206  0.001120 ** 
## BAL                1     0.9     0.9     1.6206  0.203025    
## BUF                1     0.8     0.8     1.3448  0.246194    
## CAR                1     0.6     0.6     1.0163  0.313413    
## CHI                1     0.0     0.0     0.0073  0.932089    
## CIN                1     0.3     0.3     0.5180  0.471689    
## CLE                1     0.0     0.0     0.0621  0.803255    
## DET                1    21.4    21.4    37.2209 1.069e-09 ***
## HOU                1     1.1     1.1     1.8455  0.174323    
## IND                1    11.6    11.6    20.1547 7.171e-06 ***
## JAC                1     2.0     2.0     3.4702  0.062494 .  
## KC                 1     6.0     6.0    10.4925  0.001200 ** 
## MIA                1     0.7     0.7     1.2103  0.271286    
## MINN               1     1.0     1.0     1.7083  0.191223    
## NYG                1     3.7     3.7     6.3533  0.011722 *  
## NYJ                1     0.6     0.6     1.1157  0.290857    
## OAK                1     1.0     1.0     1.7412  0.186993    
## PHI                1     3.8     3.8     6.6112  0.010139 *  
## PIT                1     5.0     5.0     8.7286  0.003135 ** 
## SD                 1     1.0     1.0     1.7287  0.188586    
## STL                1     3.0     3.0     5.1518  0.023230 *  
## TB                 1     0.5     0.5     0.7916  0.373618    
## TEN                1     3.7     3.7     6.4768  0.010935 *  
## WAS                1     0.6     0.6     1.0442  0.306864    
## avg_rectd_plyr     1 10771.0 10771.0 18744.1659 < 2.2e-16 ***
## avg_rbry_plyr      1    74.1    74.1   128.9315 < 2.2e-16 ***
## avg_rbry_pos       1    58.0    58.0   101.0080 < 2.2e-16 ***
## avg_fuml_plyr      1   205.7   205.7   357.9520 < 2.2e-16 ***
## avg_qbtdp_plyr     1   146.7   146.7   255.2558 < 2.2e-16 ***
## Residuals      27451 15774.3     0.6                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

This one was an improvement over the previous models. It still has its problems, and may need some refinement or other variables to improve the predictions.

AIC:

aic_trg <- step(lm(trgregform, data = trainTransformedtrg), direction = "backward")
## Start:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-15244.2
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - vertical1       1       0.0 15730 -15246.2
## - bad_weather_1   1       0.0 15730 -15246.2
## - GB              1       0.7 15731 -15245.0
## - DAL             1       0.7 15731 -15244.9
## - hot_weather     1       0.8 15731 -15244.9
## - grass_1         1       1.1 15732 -15244.3
## <none>                        15730 -15244.2
## - cold_weather    1       1.3 15732 -15244.0
## - NOR             1       1.7 15732 -15243.2
## - SEA             1       2.0 15732 -15242.8
## - DEN             1       2.1 15733 -15242.5
## - NE              1       2.4 15733 -15242.0
## - height          1       2.9 15733 -15241.2
## - avg_fuml_plyr   1       6.0 15736 -15235.7
## - SD              1       6.5 15737 -15234.8
## - home_team_1     1       6.6 15737 -15234.6
## - CAR             1       7.2 15738 -15233.7
## - TB              1       8.0 15738 -15232.2
## - BUF             1       8.7 15739 -15231.0
## - WAS             1       9.2 15740 -15230.2
## - TEN             1       9.2 15740 -15230.1
## - ATL             1      10.7 15741 -15227.5
## - NYJ             1      11.0 15741 -15227.0
## - PIT             1      11.5 15742 -15226.1
## - NYG             1      11.8 15742 -15225.5
## - CHI             1      12.1 15742 -15225.1
## - KC              1      12.1 15743 -15225.1
## - CIN             1      12.2 15743 -15224.9
## - MIA             1      13.2 15744 -15223.2
## - PHI             1      13.6 15744 -15222.5
## - OAK             1      14.7 15745 -15220.5
## - forty1          1      15.7 15746 -15218.7
## - STL             1      17.1 15748 -15216.3
## - IND             1      17.6 15748 -15215.5
## - MINN            1      17.8 15748 -15215.2
## - ARI             1      18.2 15749 -15214.5
## - DET             1      18.7 15749 -15213.5
## - BAL             1      21.5 15752 -15208.7
## - HOU             1      22.3 15753 -15207.3
## - JAC             1      22.6 15753 -15206.7
## - weight          1      35.2 15766 -15184.7
## - CLE             1      39.9 15770 -15176.5
## - avg_qbtdp_plyr  1      80.5 15811 -15106.0
## - avg_rbry_pos    1      99.9 15830 -15072.3
## - avg_rbry_plyr   1     126.5 15857 -15026.1
## - avg_rectd_plyr  1    5564.7 21295  -6921.8
## 
## Step:  AIC=-15246.19
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - bad_weather_1   1       0.0 15730 -15248.2
## - GB              1       0.7 15731 -15247.0
## - DAL             1       0.7 15731 -15246.9
## - hot_weather     1       0.8 15731 -15246.8
## - grass_1         1       1.1 15732 -15246.3
## <none>                        15730 -15246.2
## - cold_weather    1       1.3 15732 -15246.0
## - NOR             1       1.7 15732 -15245.2
## - SEA             1       2.0 15732 -15244.8
## - DEN             1       2.2 15733 -15244.4
## - NE              1       2.4 15733 -15244.0
## - height          1       2.9 15733 -15243.2
## - avg_fuml_plyr   1       6.0 15736 -15237.7
## - SD              1       6.5 15737 -15236.8
## - home_team_1     1       6.6 15737 -15236.6
## - CAR             1       7.2 15738 -15235.7
## - TB              1       8.0 15738 -15234.2
## - BUF             1       8.7 15739 -15233.0
## - WAS             1       9.1 15740 -15232.2
## - TEN             1       9.2 15740 -15232.1
## - ATL             1      10.7 15741 -15229.5
## - NYJ             1      11.0 15742 -15229.0
## - PIT             1      11.5 15742 -15228.1
## - NYG             1      11.8 15742 -15227.5
## - CHI             1      12.1 15743 -15227.1
## - KC              1      12.1 15743 -15227.1
## - CIN             1      12.2 15743 -15226.9
## - MIA             1      13.2 15744 -15225.2
## - PHI             1      13.6 15744 -15224.5
## - OAK             1      14.7 15745 -15222.5
## - STL             1      17.1 15748 -15218.3
## - IND             1      17.6 15748 -15217.5
## - MINN            1      17.8 15748 -15217.1
## - ARI             1      18.2 15749 -15216.5
## - DET             1      18.7 15749 -15215.5
## - BAL             1      21.5 15752 -15210.7
## - forty1          1      22.0 15752 -15209.8
## - HOU             1      22.3 15753 -15209.3
## - JAC             1      22.7 15753 -15208.6
## - weight          1      35.3 15766 -15186.5
## - CLE             1      40.0 15770 -15178.5
## - avg_qbtdp_plyr  1      80.5 15811 -15107.9
## - avg_rbry_pos    1      99.9 15830 -15074.2
## - avg_rbry_plyr   1     126.8 15857 -15027.6
## - avg_rectd_plyr  1    5578.3 21309  -6906.2
## 
## Step:  AIC=-15248.17
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS      AIC
## - GB              1       0.7 15731 -15249.0
## - DAL             1       0.7 15731 -15248.9
## - hot_weather     1       0.8 15731 -15248.8
## - grass_1         1       1.1 15732 -15248.3
## <none>                        15730 -15248.2
## - cold_weather    1       1.3 15732 -15247.9
## - NOR             1       1.7 15732 -15247.1
## - SEA             1       2.0 15732 -15246.7
## - DEN             1       2.2 15733 -15246.4
## - NE              1       2.4 15733 -15246.0
## - height          1       2.9 15733 -15245.2
## - avg_fuml_plyr   1       6.0 15736 -15239.7
## - SD              1       6.6 15737 -15238.7
## - home_team_1     1       6.7 15737 -15238.6
## - CAR             1       7.2 15738 -15237.7
## - TB              1       8.0 15738 -15236.1
## - BUF             1       8.7 15739 -15235.0
## - WAS             1       9.1 15740 -15234.2
## - TEN             1       9.2 15740 -15234.0
## - ATL             1      10.7 15741 -15231.5
## - NYJ             1      11.0 15742 -15231.0
## - PIT             1      11.5 15742 -15230.0
## - NYG             1      11.8 15742 -15229.5
## - CHI             1      12.1 15743 -15229.1
## - KC              1      12.1 15743 -15229.0
## - CIN             1      12.2 15743 -15228.9
## - MIA             1      13.2 15744 -15227.2
## - PHI             1      13.6 15744 -15226.5
## - OAK             1      14.7 15745 -15224.5
## - STL             1      17.2 15748 -15220.2
## - IND             1      17.6 15748 -15219.5
## - MINN            1      17.8 15748 -15219.1
## - ARI             1      18.2 15749 -15218.4
## - DET             1      18.7 15749 -15217.4
## - BAL             1      21.5 15752 -15212.6
## - forty1          1      22.0 15752 -15211.8
## - HOU             1      22.3 15753 -15211.3
## - JAC             1      22.7 15753 -15210.5
## - weight          1      35.3 15766 -15188.5
## - CLE             1      39.9 15770 -15180.5
## - avg_qbtdp_plyr  1      80.5 15811 -15109.9
## - avg_rbry_pos    1      99.9 15830 -15076.1
## - avg_rbry_plyr   1     126.8 15857 -15029.6
## - avg_rectd_plyr  1    5578.7 21309  -6907.7
## 
## Step:  AIC=-15248.99
## trg ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS      AIC
## - hot_weather     1       0.8 15732 -15249.6
## - grass_1         1       1.1 15732 -15249.1
## <none>                        15731 -15249.0
## - SEA             1       1.3 15732 -15248.7
## - cold_weather    1       1.5 15733 -15248.4
## - DAL             1       2.1 15733 -15247.3
## - height          1       2.8 15734 -15246.0
## - NOR             1       4.1 15735 -15243.8
## - DEN             1       4.8 15736 -15242.5
## - NE              1       5.3 15736 -15241.7
## - avg_fuml_plyr   1       5.9 15737 -15240.6
## - home_team_1     1       6.6 15738 -15239.4
## - SD              1      11.7 15743 -15230.6
## - CAR             1      12.7 15744 -15228.8
## - TB              1      13.9 15745 -15226.8
## - BUF             1      14.9 15746 -15225.0
## - WAS             1      15.8 15747 -15223.4
## - TEN             1      15.8 15747 -15223.4
## - ATL             1      18.0 15749 -15219.6
## - NYJ             1      18.5 15750 -15218.7
## - PIT             1      19.7 15751 -15216.6
## - CHI             1      19.8 15751 -15216.3
## - NYG             1      19.9 15751 -15216.2
## - CIN             1      20.2 15751 -15215.7
## - KC              1      20.3 15752 -15215.6
## - MIA             1      21.6 15753 -15213.3
## - PHI             1      22.1 15753 -15212.4
## - forty1          1      22.2 15753 -15212.3
## - OAK             1      24.2 15755 -15208.8
## - STL             1      27.0 15758 -15203.9
## - MINN            1      28.0 15759 -15202.1
## - IND             1      28.1 15759 -15201.9
## - ARI             1      28.7 15760 -15200.9
## - DET             1      29.5 15761 -15199.5
## - BAL             1      34.5 15766 -15190.8
## - HOU             1      34.7 15766 -15190.3
## - JAC             1      35.1 15766 -15189.6
## - weight          1      35.3 15766 -15189.4
## - CLE             1      60.1 15791 -15146.1
## - avg_qbtdp_plyr  1      81.2 15812 -15109.4
## - avg_rbry_pos    1     100.4 15832 -15076.1
## - avg_rbry_plyr   1     126.7 15858 -15030.4
## - avg_rectd_plyr  1    5600.2 21331  -6881.1
## 
## Step:  AIC=-15249.63
## trg ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS      AIC
## <none>                        15732 -15249.6
## - grass_1         1       1.3 15733 -15249.4
## - cold_weather    1       1.4 15733 -15249.1
## - SEA             1       1.4 15733 -15249.1
## - DAL             1       2.1 15734 -15248.0
## - height          1       2.9 15735 -15246.6
## - NOR             1       4.0 15736 -15244.6
## - DEN             1       4.8 15737 -15243.3
## - NE              1       5.2 15737 -15242.5
## - avg_fuml_plyr   1       5.9 15738 -15241.3
## - home_team_1     1       6.6 15738 -15240.1
## - SD              1      11.4 15743 -15231.7
## - CAR             1      12.7 15745 -15229.4
## - TB              1      13.7 15746 -15227.8
## - BUF             1      14.7 15747 -15226.0
## - WAS             1      15.8 15748 -15224.1
## - TEN             1      15.8 15748 -15224.0
## - ATL             1      17.9 15750 -15220.3
## - NYJ             1      18.2 15750 -15219.9
## - PIT             1      19.5 15752 -15217.5
## - NYG             1      19.8 15752 -15217.0
## - CHI             1      19.9 15752 -15217.0
## - CIN             1      20.1 15752 -15216.5
## - KC              1      20.3 15752 -15216.2
## - MIA             1      21.6 15754 -15213.9
## - PHI             1      22.1 15754 -15213.0
## - forty1          1      22.2 15754 -15212.9
## - OAK             1      24.2 15756 -15209.3
## - STL             1      26.7 15759 -15205.1
## - MINN            1      27.9 15760 -15202.8
## - IND             1      28.0 15760 -15202.7
## - ARI             1      28.7 15761 -15201.6
## - DET             1      29.5 15761 -15200.2
## - BAL             1      34.4 15766 -15191.6
## - HOU             1      34.7 15767 -15191.1
## - weight          1      35.2 15767 -15190.2
## - JAC             1      35.2 15767 -15190.2
## - CLE             1      60.2 15792 -15146.7
## - avg_qbtdp_plyr  1      81.2 15813 -15110.2
## - avg_rbry_pos    1     100.4 15832 -15076.8
## - avg_rbry_plyr   1     126.6 15858 -15031.3
## - avg_rectd_plyr  1    5600.4 21332  -6881.9

Receiving TD’s

PreProcess:

set.seed(123)
splittdrec <- sample.split(nfl_data$tdrec, SplitRatio = 0.7)
Traintdrec <- subset(nfl_data, split == TRUE)
Testtdrec <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Traintdrec, method = c("center", "scale"))
trainTransformedtdrec <- predict(preProcValues, Traintdrec)
testTransformedtdrec <- predict(preProcValues, Testtdrec)

ggpairs:

ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("tdrec",colnames(filtered_nfl_data_fields[46:51]))])

tdrecregform <- formula(paste("tdrec ~ ", 
                            paste(colnames(filtered_nfl_data_fields), collapse="+")))


linRegRecTD <- lm(tdrecregform, data = trainTransformedtdrec)

summary(linRegRecTD)
## 
## Call:
## lm(formula = tdrecregform, data = trainTransformedtdrec)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0021 -0.4352 -0.1339 -0.0007  9.0491 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -7.581e-16  5.564e-03   0.000   1.0000    
## height          -1.859e-03  1.080e-02  -0.172   0.8633    
## weight           3.922e-03  1.012e-02   0.388   0.6983    
## cold_weather    -2.811e-03  5.857e-03  -0.480   0.6312    
## hot_weather     -4.891e-03  5.615e-03  -0.871   0.3837    
## home_team_1      1.117e-02  6.054e-03   1.845   0.0651 .  
## forty1           3.616e-04  9.602e-03   0.038   0.9700    
## vertical1       -4.348e-04  7.383e-03  -0.059   0.9530    
## ARI              7.210e-03  7.783e-03   0.926   0.3542    
## ATL              1.778e-02  7.821e-03   2.273   0.0230 *  
## BAL              1.095e-02  7.827e-03   1.399   0.1618    
## BUF              1.508e-02  7.727e-03   1.951   0.0510 .  
## CAR              1.471e-02  7.676e-03   1.916   0.0554 .  
## CHI              1.662e-02  7.590e-03   2.189   0.0286 *  
## CIN              1.403e-02  7.730e-03   1.815   0.0695 .  
## CLE              7.259e-03  7.695e-03   0.943   0.3455    
## DAL              1.531e-02  7.773e-03   1.970   0.0489 *  
## DEN              1.319e-02  7.802e-03   1.691   0.0909 .  
## DET              1.178e-02  7.695e-03   1.530   0.1259    
## GB               1.357e-02  7.922e-03   1.714   0.0866 .  
## HOU              9.462e-03  7.827e-03   1.209   0.2267    
## IND              1.545e-02  7.770e-03   1.989   0.0467 *  
## JAC              1.234e-02  7.580e-03   1.629   0.1034    
## KC               1.290e-02  7.746e-03   1.666   0.0958 .  
## MIA              6.369e-03  7.621e-03   0.836   0.4033    
## MINN             6.372e-03  7.668e-03   0.831   0.4059    
## NE               1.092e-02  8.008e-03   1.364   0.1726    
## NOR              2.257e-02  7.983e-03   2.827   0.0047 ** 
## NYG              1.288e-02  7.803e-03   1.650   0.0989 .  
## NYJ              7.421e-03  7.774e-03   0.955   0.3398    
## OAK              1.286e-02  7.823e-03   1.643   0.1003    
## PHI              6.709e-03  7.581e-03   0.885   0.3762    
## PIT              1.512e-02  7.780e-03   1.943   0.0520 .  
## SD               1.438e-02  7.635e-03   1.884   0.0596 .  
## SEA              8.028e-03  7.923e-03   1.013   0.3110    
## STL              5.368e-03  7.712e-03   0.696   0.4864    
## TB               1.070e-02  7.640e-03   1.401   0.1612    
## TEN              1.366e-02  7.686e-03   1.778   0.0755 .  
## WAS              1.131e-02  7.727e-03   1.463   0.1434    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr   3.863e-01  7.105e-03  54.366   <2e-16 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr   -2.765e-03  8.503e-03  -0.325   0.7450    
## avg_rbry_pos     3.315e-03  9.907e-03   0.335   0.7379    
## avg_fuml_plyr    1.343e-03  8.219e-03   0.163   0.8702    
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -1.978e-03  8.928e-03  -0.222   0.8247    
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -5.577e-03  6.402e-03  -0.871   0.3837    
## bad_weather_1    1.094e-02  5.660e-03   1.933   0.0533 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9224 on 27438 degrees of freedom
## Multiple R-squared:  0.1505, Adjusted R-squared:  0.1491 
## F-statistic: 108.1 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegRecTD2 <- update(linRegRecTD, ~. -height-weight-cold_weather-hot_weather-home_team_1
                       -forty1-is_WR-is_TE-age-vertical1-ARI-BAL-BUF-CAR-CIN-CLE-DAL-DEN-DET-GB
                       -HOU-IND-JAC-KC-MIA-MINN-NE-NYG-NYJ-OAK-PHI-PIT-SEA-STL-TB-TEN-WAS
                       -avg_trg_team -avg_tdr_team-avg_rbra_team-avg_rbry_plyr
                       -avg_rbry_pos-avg_fuml_plyr-avg_fuml_team-avg_qbints_plyr_avg_qbtdp_team 
                       -avg_qbints_team - grass_1-bad_weather_1)

summary(linRegRecTD2)
## 
## Call:
## lm(formula = tdrec ~ ATL + CHI + NOR + SD + avg_rectd_plyr + 
##     avg_qbtdp_plyr + avg_qbtdp_team, data = trainTransformedtdrec)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9578 -0.4394 -0.1323  0.0057  9.0814 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -5.458e-16  5.562e-03   0.000   1.0000    
## ATL             3.963e-03  5.688e-03   0.697   0.4860    
## CHI             6.058e-03  5.575e-03   1.087   0.2772    
## NOR             6.674e-03  6.066e-03   1.100   0.2713    
## SD              8.847e-04  5.737e-03   0.154   0.8775    
## avg_rectd_plyr  3.840e-01  5.942e-03  64.613   <2e-16 ***
## avg_qbtdp_plyr -1.707e-03  5.877e-03  -0.291   0.7714    
## avg_qbtdp_team  1.171e-02  6.388e-03   1.834   0.0667 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9221 on 27476 degrees of freedom
## Multiple R-squared:  0.1499, Adjusted R-squared:  0.1497 
## F-statistic: 692.4 on 7 and 27476 DF,  p-value: < 2.2e-16
linRegRecTD3 <- update(linRegRecTD2, ~. -ATL-CHI-NOR-SD-avg_qbints_plyr-avg_qbints_team)

summary(linRegRecTD3)
## 
## Call:
## lm(formula = tdrec ~ avg_rectd_plyr + avg_qbtdp_plyr + avg_qbtdp_team, 
##     data = trainTransformedtdrec)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.9629 -0.4373 -0.1342  0.0040  9.0780 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -5.147e-16  5.562e-03   0.000  1.00000    
## avg_rectd_plyr  3.839e-01  5.941e-03  64.611  < 2e-16 ***
## avg_qbtdp_plyr -1.732e-03  5.876e-03  -0.295  0.76822    
## avg_qbtdp_team  1.505e-02  5.686e-03   2.647  0.00811 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9221 on 27480 degrees of freedom
## Multiple R-squared:  0.1499, Adjusted R-squared:  0.1498 
## F-statistic:  1615 on 3 and 27480 DF,  p-value: < 2.2e-16

The R2 is worsened in the second model, and the third. (the R2 in general is fairly low)

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

RectdPredicted <- predict(linRegRecTD3, newdata = testTransformedtdrec)

SSErectd <- sum((RectdPredicted - testTransformedtdrec$tdrec)^2)
SSTrectd <- sum((mean(nfl_data$tdrec)-testTransformedtdrec$tdrec)^2)
r2_rectd <- 1 - SSErectd/SSTrectd 
r2_rectd
## [1] 0.1697301
rmse_rectd <- sqrt(SSEtrg/nrow(testTransformedtdrec))
rmse_rectd
## [1] 0.7421937

Regression plots below

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegRecTD3, which = c(1:3,5))

I would say that it appears that these charts do not like the prediction. Touchdowns are infrequent and random/unpredictable. If a receiver has an amazing season and gets 100 receptions, if they had 10 Tds it would be an All-pro year for them.

Additional summary statistics

confint(linRegRecTD3)
##                       2.5 %     97.5 %
## (Intercept)    -0.010901714 0.01090171
## avg_rectd_plyr  0.372215276 0.39550490
## avg_qbtdp_plyr -0.013249830 0.00978614
## avg_qbtdp_team  0.003908858 0.02619924
coef(summary(linRegRecTD3))
##                     Estimate  Std. Error       t value    Pr(>|t|)
## (Intercept)    -5.146925e-16 0.005561956 -9.253804e-14 1.000000000
## avg_rectd_plyr  3.838601e-01 0.005941078  6.461119e+01 0.000000000
## avg_qbtdp_plyr -1.731845e-03 0.005876372 -2.947133e-01 0.768215113
## avg_qbtdp_team  1.505405e-02 0.005686176  2.647482e+00 0.008113993
anova(linRegRecTD3)
## Analysis of Variance Table
## 
## Response: tdrec
##                   Df  Sum Sq Mean Sq   F value    Pr(>F)    
## avg_rectd_plyr     1  4112.8  4112.8 4837.2842 < 2.2e-16 ***
## avg_qbtdp_plyr     1     0.0     0.0    0.0023  0.961434    
## avg_qbtdp_team     1     6.0     6.0    7.0092  0.008114 ** 
## Residuals      27480 23364.2     0.9                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_tdrec <- step(lm(tdrecregform, data = trainTransformedtdrec), direction = "backward")
## Start:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-4392.92
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - forty1          1      0.00 23346 -4394.9
## - vertical1       1      0.00 23346 -4394.9
## - avg_fuml_plyr   1      0.02 23346 -4394.9
## - height          1      0.03 23346 -4394.9
## - avg_qbtdp_plyr  1      0.04 23346 -4394.9
## - avg_rbry_plyr   1      0.09 23346 -4394.8
## - avg_rbry_pos    1      0.10 23346 -4394.8
## - weight          1      0.13 23346 -4394.8
## - cold_weather    1      0.20 23346 -4394.7
## - STL             1      0.41 23346 -4394.4
## - MINN            1      0.59 23347 -4394.2
## - MIA             1      0.59 23347 -4394.2
## - hot_weather     1      0.65 23347 -4394.2
## - grass_1         1      0.65 23347 -4394.2
## - PHI             1      0.67 23347 -4394.1
## - ARI             1      0.73 23347 -4394.1
## - CLE             1      0.76 23347 -4394.0
## - NYJ             1      0.78 23347 -4394.0
## - SEA             1      0.87 23347 -4393.9
## - HOU             1      1.24 23347 -4393.5
## - NE              1      1.58 23348 -4393.1
## - BAL             1      1.67 23348 -4393.0
## - TB              1      1.67 23348 -4392.9
## <none>                        23346 -4392.9
## - WAS             1      1.82 23348 -4392.8
## - DET             1      1.99 23348 -4392.6
## - JAC             1      2.26 23348 -4392.3
## - OAK             1      2.30 23348 -4392.2
## - NYG             1      2.32 23348 -4392.2
## - KC              1      2.36 23348 -4392.1
## - DEN             1      2.43 23348 -4392.1
## - GB              1      2.50 23348 -4392.0
## - TEN             1      2.69 23349 -4391.8
## - CIN             1      2.80 23349 -4391.6
## - home_team_1     1      2.89 23349 -4391.5
## - SD              1      3.02 23349 -4391.4
## - CAR             1      3.12 23349 -4391.2
## - bad_weather_1   1      3.18 23349 -4391.2
## - PIT             1      3.21 23349 -4391.1
## - BUF             1      3.24 23349 -4391.1
## - DAL             1      3.30 23349 -4391.0
## - IND             1      3.37 23349 -4391.0
## - CHI             1      4.08 23350 -4390.1
## - ATL             1      4.40 23350 -4389.7
## - NOR             1      6.80 23353 -4386.9
## - avg_rectd_plyr  1   2514.88 25861 -1583.1
## 
## Step:  AIC=-4394.91
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - vertical1       1      0.01 23346 -4396.9
## - avg_fuml_plyr   1      0.02 23346 -4396.9
## - height          1      0.03 23346 -4396.9
## - avg_qbtdp_plyr  1      0.04 23346 -4396.9
## - avg_rbry_pos    1      0.09 23346 -4396.8
## - avg_rbry_plyr   1      0.10 23346 -4396.8
## - weight          1      0.16 23346 -4396.7
## - cold_weather    1      0.20 23346 -4396.7
## - STL             1      0.41 23346 -4396.4
## - MINN            1      0.59 23347 -4396.2
## - MIA             1      0.59 23347 -4396.2
## - hot_weather     1      0.65 23347 -4396.2
## - grass_1         1      0.65 23347 -4396.2
## - PHI             1      0.67 23347 -4396.1
## - ARI             1      0.73 23347 -4396.1
## - CLE             1      0.76 23347 -4396.0
## - NYJ             1      0.78 23347 -4396.0
## - SEA             1      0.87 23347 -4395.9
## - HOU             1      1.25 23347 -4395.4
## - NE              1      1.60 23348 -4395.0
## - BAL             1      1.66 23348 -4395.0
## - TB              1      1.67 23348 -4394.9
## <none>                        23346 -4394.9
## - WAS             1      1.82 23348 -4394.8
## - DET             1      1.99 23348 -4394.6
## - JAC             1      2.26 23348 -4394.3
## - OAK             1      2.30 23348 -4394.2
## - NYG             1      2.32 23348 -4394.2
## - KC              1      2.36 23348 -4394.1
## - DEN             1      2.43 23348 -4394.0
## - GB              1      2.50 23348 -4394.0
## - TEN             1      2.69 23349 -4393.7
## - CIN             1      2.80 23349 -4393.6
## - home_team_1     1      2.89 23349 -4393.5
## - SD              1      3.02 23349 -4393.4
## - CAR             1      3.12 23349 -4393.2
## - bad_weather_1   1      3.18 23349 -4393.2
## - PIT             1      3.21 23349 -4393.1
## - BUF             1      3.24 23349 -4393.1
## - DAL             1      3.30 23349 -4393.0
## - IND             1      3.36 23349 -4393.0
## - CHI             1      4.08 23350 -4392.1
## - ATL             1      4.40 23350 -4391.7
## - NOR             1      6.80 23353 -4388.9
## - avg_rectd_plyr  1   2556.93 25903 -1540.5
## 
## Step:  AIC=-4396.91
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + 
##     NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_fuml_plyr   1      0.02 23346 -4398.9
## - height          1      0.03 23346 -4398.9
## - avg_qbtdp_plyr  1      0.04 23346 -4398.9
## - avg_rbry_pos    1      0.10 23346 -4398.8
## - avg_rbry_plyr   1      0.10 23346 -4398.8
## - weight          1      0.18 23346 -4398.7
## - cold_weather    1      0.20 23346 -4398.7
## - STL             1      0.42 23346 -4398.4
## - MINN            1      0.59 23347 -4398.2
## - MIA             1      0.60 23347 -4398.2
## - hot_weather     1      0.65 23347 -4398.1
## - grass_1         1      0.65 23347 -4398.1
## - PHI             1      0.67 23347 -4398.1
## - ARI             1      0.73 23347 -4398.0
## - CLE             1      0.76 23347 -4398.0
## - NYJ             1      0.77 23347 -4398.0
## - SEA             1      0.87 23347 -4397.9
## - HOU             1      1.25 23347 -4397.4
## - NE              1      1.63 23348 -4397.0
## - BAL             1      1.67 23348 -4396.9
## - TB              1      1.68 23348 -4396.9
## <none>                        23346 -4396.9
## - WAS             1      1.82 23348 -4396.8
## - DET             1      1.99 23348 -4396.6
## - JAC             1      2.26 23348 -4396.3
## - OAK             1      2.30 23348 -4396.2
## - NYG             1      2.33 23348 -4396.2
## - KC              1      2.36 23348 -4396.1
## - DEN             1      2.43 23348 -4396.0
## - GB              1      2.51 23348 -4395.9
## - TEN             1      2.69 23349 -4395.7
## - CIN             1      2.82 23349 -4395.6
## - home_team_1     1      2.89 23349 -4395.5
## - SD              1      3.04 23349 -4395.3
## - CAR             1      3.12 23349 -4395.2
## - bad_weather_1   1      3.18 23349 -4395.2
## - PIT             1      3.22 23349 -4395.1
## - BUF             1      3.25 23349 -4395.1
## - DAL             1      3.31 23349 -4395.0
## - IND             1      3.36 23349 -4394.9
## - CHI             1      4.09 23350 -4394.1
## - ATL             1      4.44 23350 -4393.7
## - NOR             1      6.80 23353 -4390.9
## - avg_rectd_plyr  1   2604.08 25950 -1492.5
## 
## Step:  AIC=-4398.88
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + 
##     NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_qbtdp_plyr  1      0.01 23346 -4400.9
## - height          1      0.02 23346 -4400.9
## - avg_rbry_plyr   1      0.08 23346 -4400.8
## - avg_rbry_pos    1      0.10 23346 -4400.8
## - weight          1      0.17 23346 -4400.7
## - cold_weather    1      0.20 23346 -4400.6
## - STL             1      0.42 23346 -4400.4
## - MINN            1      0.59 23347 -4400.2
## - MIA             1      0.60 23347 -4400.2
## - hot_weather     1      0.65 23347 -4400.1
## - grass_1         1      0.65 23347 -4400.1
## - PHI             1      0.68 23347 -4400.1
## - ARI             1      0.74 23347 -4400.0
## - CLE             1      0.77 23347 -4400.0
## - NYJ             1      0.78 23347 -4400.0
## - SEA             1      0.87 23347 -4399.9
## - HOU             1      1.25 23347 -4399.4
## - NE              1      1.61 23348 -4399.0
## - BAL             1      1.66 23348 -4398.9
## - TB              1      1.69 23348 -4398.9
## <none>                        23346 -4398.9
## - WAS             1      1.83 23348 -4398.7
## - DET             1      2.00 23348 -4398.5
## - JAC             1      2.25 23348 -4398.2
## - OAK             1      2.30 23348 -4398.2
## - NYG             1      2.34 23348 -4398.1
## - KC              1      2.37 23348 -4398.1
## - DEN             1      2.44 23348 -4398.0
## - GB              1      2.50 23348 -4397.9
## - TEN             1      2.70 23349 -4397.7
## - CIN             1      2.82 23349 -4397.6
## - home_team_1     1      2.90 23349 -4397.5
## - SD              1      3.05 23349 -4397.3
## - CAR             1      3.12 23349 -4397.2
## - bad_weather_1   1      3.18 23349 -4397.1
## - PIT             1      3.23 23349 -4397.1
## - BUF             1      3.26 23349 -4397.0
## - DAL             1      3.31 23349 -4397.0
## - IND             1      3.36 23349 -4396.9
## - CHI             1      4.12 23350 -4396.0
## - ATL             1      4.42 23350 -4395.7
## - NOR             1      6.79 23353 -4392.9
## - avg_rectd_plyr  1   2605.85 25952 -1492.6
## 
## Step:  AIC=-4400.86
## tdrec ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + 
##     NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - height          1      0.05 23346 -4402.8
## - avg_rbry_plyr   1      0.08 23346 -4402.8
## - avg_rbry_pos    1      0.09 23346 -4402.8
## - cold_weather    1      0.20 23346 -4402.6
## - weight          1      0.21 23346 -4402.6
## - STL             1      0.43 23346 -4402.4
## - MINN            1      0.60 23347 -4402.2
## - MIA             1      0.60 23347 -4402.1
## - hot_weather     1      0.64 23347 -4402.1
## - grass_1         1      0.65 23347 -4402.1
## - PHI             1      0.68 23347 -4402.1
## - ARI             1      0.74 23347 -4402.0
## - CLE             1      0.77 23347 -4401.9
## - NYJ             1      0.79 23347 -4401.9
## - SEA             1      0.86 23347 -4401.8
## - HOU             1      1.26 23347 -4401.4
## - NE              1      1.60 23348 -4401.0
## - BAL             1      1.67 23348 -4400.9
## - TB              1      1.69 23348 -4400.9
## <none>                        23346 -4400.9
## - WAS             1      1.83 23348 -4400.7
## - DET             1      2.00 23348 -4400.5
## - JAC             1      2.26 23348 -4400.2
## - OAK             1      2.31 23348 -4400.1
## - NYG             1      2.33 23348 -4400.1
## - KC              1      2.38 23348 -4400.1
## - DEN             1      2.43 23348 -4400.0
## - GB              1      2.49 23348 -4399.9
## - TEN             1      2.71 23349 -4399.7
## - CIN             1      2.82 23349 -4399.5
## - home_team_1     1      2.90 23349 -4399.4
## - SD              1      3.04 23349 -4399.3
## - CAR             1      3.12 23349 -4399.2
## - bad_weather_1   1      3.18 23349 -4399.1
## - PIT             1      3.23 23349 -4399.1
## - BUF             1      3.28 23349 -4399.0
## - DAL             1      3.30 23349 -4399.0
## - IND             1      3.35 23349 -4398.9
## - CHI             1      4.13 23350 -4398.0
## - ATL             1      4.41 23350 -4397.7
## - NOR             1      6.77 23353 -4394.9
## - avg_rectd_plyr  1   3038.70 26385 -1039.9
## 
## Step:  AIC=-4402.81
## tdrec ~ weight + cold_weather + hot_weather + home_team_1 + ARI + 
##     ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_rbry_plyr   1      0.08 23346 -4404.7
## - cold_weather    1      0.20 23346 -4404.6
## - weight          1      0.21 23346 -4404.6
## - avg_rbry_pos    1      0.23 23346 -4404.5
## - STL             1      0.42 23346 -4404.3
## - MINN            1      0.58 23347 -4404.1
## - MIA             1      0.60 23347 -4404.1
## - hot_weather     1      0.65 23347 -4404.0
## - grass_1         1      0.65 23347 -4404.0
## - PHI             1      0.68 23347 -4404.0
## - ARI             1      0.73 23347 -4403.9
## - CLE             1      0.77 23347 -4403.9
## - NYJ             1      0.78 23347 -4403.9
## - SEA             1      0.86 23347 -4403.8
## - HOU             1      1.24 23347 -4403.3
## - NE              1      1.60 23348 -4402.9
## - BAL             1      1.66 23348 -4402.9
## - TB              1      1.67 23348 -4402.8
## <none>                        23346 -4402.8
## - WAS             1      1.85 23348 -4402.6
## - DET             1      1.98 23348 -4402.5
## - JAC             1      2.25 23348 -4402.2
## - OAK             1      2.28 23348 -4402.1
## - NYG             1      2.31 23348 -4402.1
## - KC              1      2.36 23348 -4402.0
## - DEN             1      2.42 23348 -4402.0
## - GB              1      2.48 23349 -4401.9
## - TEN             1      2.69 23349 -4401.6
## - CIN             1      2.79 23349 -4401.5
## - home_team_1     1      2.90 23349 -4401.4
## - SD              1      3.01 23349 -4401.3
## - CAR             1      3.12 23349 -4401.1
## - bad_weather_1   1      3.18 23349 -4401.1
## - PIT             1      3.21 23349 -4401.0
## - BUF             1      3.25 23349 -4401.0
## - DAL             1      3.28 23349 -4400.9
## - IND             1      3.36 23349 -4400.9
## - CHI             1      4.09 23350 -4400.0
## - ATL             1      4.41 23350 -4399.6
## - NOR             1      6.75 23353 -4396.9
## - avg_rectd_plyr  1   3044.09 26390 -1036.3
## 
## Step:  AIC=-4404.71
## tdrec ~ weight + cold_weather + hot_weather + home_team_1 + ARI + 
##     ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_rbry_pos    1      0.15 23346 -4406.5
## - cold_weather    1      0.19 23346 -4406.5
## - weight          1      0.23 23346 -4406.4
## - STL             1      0.43 23347 -4406.2
## - MINN            1      0.58 23347 -4406.0
## - MIA             1      0.61 23347 -4406.0
## - grass_1         1      0.65 23347 -4405.9
## - hot_weather     1      0.65 23347 -4405.9
## - PHI             1      0.67 23347 -4405.9
## - ARI             1      0.74 23347 -4405.8
## - NYJ             1      0.78 23347 -4405.8
## - CLE             1      0.78 23347 -4405.8
## - SEA             1      0.86 23347 -4405.7
## - HOU             1      1.24 23347 -4405.2
## - NE              1      1.61 23348 -4404.8
## - BAL             1      1.68 23348 -4404.7
## - TB              1      1.69 23348 -4404.7
## <none>                        23346 -4404.7
## - WAS             1      1.86 23348 -4404.5
## - DET             1      2.02 23348 -4404.3
## - JAC             1      2.27 23348 -4404.0
## - OAK             1      2.31 23348 -4404.0
## - NYG             1      2.34 23348 -4404.0
## - KC              1      2.37 23348 -4403.9
## - DEN             1      2.44 23349 -4403.8
## - GB              1      2.49 23349 -4403.8
## - TEN             1      2.71 23349 -4403.5
## - CIN             1      2.80 23349 -4403.4
## - home_team_1     1      2.90 23349 -4403.3
## - SD              1      3.04 23349 -4403.1
## - CAR             1      3.11 23349 -4403.0
## - bad_weather_1   1      3.17 23349 -4403.0
## - PIT             1      3.22 23349 -4402.9
## - BUF             1      3.25 23349 -4402.9
## - DAL             1      3.29 23349 -4402.8
## - IND             1      3.37 23349 -4402.7
## - CHI             1      4.09 23350 -4401.9
## - ATL             1      4.45 23351 -4401.5
## - NOR             1      6.81 23353 -4398.7
## - avg_rectd_plyr  1   3050.16 26396 -1031.9
## 
## Step:  AIC=-4406.53
## tdrec ~ weight + cold_weather + hot_weather + home_team_1 + ARI + 
##     ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - cold_weather    1       0.2 23346 -4408.3
## - weight          1       0.2 23346 -4408.3
## - STL             1       0.4 23347 -4408.0
## - MINN            1       0.6 23347 -4407.9
## - MIA             1       0.6 23347 -4407.8
## - grass_1         1       0.6 23347 -4407.8
## - hot_weather     1       0.7 23347 -4407.8
## - PHI             1       0.7 23347 -4407.7
## - ARI             1       0.7 23347 -4407.7
## - CLE             1       0.8 23347 -4407.6
## - NYJ             1       0.8 23347 -4407.6
## - SEA             1       0.9 23347 -4407.5
## - HOU             1       1.2 23348 -4407.1
## - NE              1       1.6 23348 -4406.6
## - BAL             1       1.7 23348 -4406.6
## - TB              1       1.7 23348 -4406.6
## <none>                        23346 -4406.5
## - WAS             1       1.8 23348 -4406.4
## - DET             1       2.0 23348 -4406.1
## - JAC             1       2.3 23349 -4405.9
## - OAK             1       2.3 23349 -4405.8
## - NYG             1       2.3 23349 -4405.8
## - KC              1       2.4 23349 -4405.7
## - DEN             1       2.4 23349 -4405.7
## - GB              1       2.5 23349 -4405.6
## - TEN             1       2.7 23349 -4405.4
## - CIN             1       2.8 23349 -4405.3
## - home_team_1     1       2.9 23349 -4405.1
## - SD              1       3.1 23349 -4404.9
## - CAR             1       3.1 23349 -4404.9
## - bad_weather_1   1       3.2 23349 -4404.8
## - PIT             1       3.2 23349 -4404.7
## - BUF             1       3.3 23350 -4404.7
## - DAL             1       3.3 23350 -4404.7
## - IND             1       3.4 23350 -4404.6
## - CHI             1       4.1 23350 -4403.7
## - ATL             1       4.5 23351 -4403.3
## - NOR             1       6.9 23353 -4400.4
## - avg_rectd_plyr  1    3957.8 27304  -104.6
## 
## Step:  AIC=-4408.31
## tdrec ~ weight + hot_weather + home_team_1 + ARI + ATL + BAL + 
##     BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + 
##     IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + PIT + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - weight          1       0.2 23347 -4410.0
## - STL             1       0.4 23347 -4409.8
## - MINN            1       0.5 23347 -4409.7
## - MIA             1       0.6 23347 -4409.6
## - hot_weather     1       0.6 23347 -4409.6
## - PHI             1       0.6 23347 -4409.6
## - grass_1         1       0.7 23347 -4409.5
## - CLE             1       0.7 23347 -4409.5
## - ARI             1       0.7 23347 -4409.5
## - NYJ             1       0.7 23347 -4409.4
## - SEA             1       0.8 23347 -4409.4
## - HOU             1       1.2 23348 -4408.9
## - NE              1       1.6 23348 -4408.5
## - BAL             1       1.6 23348 -4408.4
## - TB              1       1.7 23348 -4408.3
## <none>                        23346 -4408.3
## - WAS             1       1.8 23348 -4408.2
## - DET             1       2.0 23349 -4407.9
## - NYG             1       2.3 23349 -4407.6
## - JAC             1       2.3 23349 -4407.6
## - KC              1       2.3 23349 -4407.6
## - OAK             1       2.3 23349 -4407.6
## - DEN             1       2.4 23349 -4407.5
## - GB              1       2.4 23349 -4407.5
## - TEN             1       2.7 23349 -4407.2
## - CIN             1       2.7 23349 -4407.1
## - home_team_1     1       2.8 23349 -4407.0
## - bad_weather_1   1       3.0 23350 -4406.7
## - SD              1       3.1 23350 -4406.7
## - CAR             1       3.1 23350 -4406.7
## - PIT             1       3.1 23350 -4406.6
## - BUF             1       3.2 23350 -4406.6
## - DAL             1       3.3 23350 -4406.4
## - IND             1       3.3 23350 -4406.4
## - CHI             1       4.0 23350 -4405.6
## - ATL             1       4.5 23351 -4405.0
## - NOR             1       6.9 23353 -4402.2
## - avg_rectd_plyr  1    3958.6 27305  -105.5
## 
## Step:  AIC=-4410.04
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + 
##     SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - STL             1       0.4 23347 -4411.6
## - MINN            1       0.5 23347 -4411.4
## - MIA             1       0.6 23347 -4411.3
## - PHI             1       0.6 23347 -4411.3
## - hot_weather     1       0.6 23347 -4411.3
## - grass_1         1       0.7 23347 -4411.2
## - CLE             1       0.7 23347 -4411.2
## - NYJ             1       0.7 23347 -4411.2
## - ARI             1       0.7 23347 -4411.2
## - SEA             1       0.8 23347 -4411.1
## - HOU             1       1.2 23348 -4410.6
## - NE              1       1.6 23348 -4410.2
## - BAL             1       1.6 23348 -4410.1
## <none>                        23347 -4410.0
## - TB              1       1.7 23348 -4410.0
## - WAS             1       1.8 23348 -4410.0
## - DET             1       2.0 23349 -4409.6
## - JAC             1       2.3 23349 -4409.4
## - KC              1       2.3 23349 -4409.4
## - NYG             1       2.3 23349 -4409.4
## - OAK             1       2.3 23349 -4409.3
## - DEN             1       2.3 23349 -4409.3
## - GB              1       2.4 23349 -4409.2
## - TEN             1       2.6 23349 -4408.9
## - CIN             1       2.7 23349 -4408.9
## - home_team_1     1       2.8 23349 -4408.7
## - bad_weather_1   1       3.1 23350 -4408.5
## - SD              1       3.1 23350 -4408.4
## - CAR             1       3.1 23350 -4408.4
## - PIT             1       3.1 23350 -4408.4
## - BUF             1       3.1 23350 -4408.3
## - DAL             1       3.3 23350 -4408.2
## - IND             1       3.3 23350 -4408.2
## - CHI             1       4.0 23351 -4407.4
## - ATL             1       4.5 23351 -4406.8
## - NOR             1       6.9 23354 -4404.0
## - avg_rectd_plyr  1    3958.4 27305  -107.5
## 
## Step:  AIC=-4411.57
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + 
##     SD + SEA + TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - MINN            1       0.2 23347 -4413.3
## - MIA             1       0.3 23347 -4413.2
## - PHI             1       0.3 23347 -4413.2
## - CLE             1       0.4 23347 -4413.1
## - ARI             1       0.4 23347 -4413.1
## - NYJ             1       0.4 23347 -4413.1
## - SEA             1       0.4 23348 -4413.1
## - hot_weather     1       0.6 23348 -4412.9
## - grass_1         1       0.8 23348 -4412.7
## - HOU             1       0.9 23348 -4412.6
## - NE              1       1.2 23348 -4412.2
## - BAL             1       1.2 23348 -4412.1
## - TB              1       1.3 23348 -4412.0
## - WAS             1       1.4 23348 -4412.0
## - DET             1       1.6 23349 -4411.6
## <none>                        23347 -4411.6
## - JAC             1       1.9 23349 -4411.4
## - KC              1       1.9 23349 -4411.4
## - NYG             1       1.9 23349 -4411.3
## - OAK             1       1.9 23349 -4411.3
## - DEN             1       2.0 23349 -4411.3
## - GB              1       2.1 23349 -4411.2
## - TEN             1       2.3 23349 -4410.9
## - CIN             1       2.3 23349 -4410.9
## - home_team_1     1       2.6 23350 -4410.5
## - SD              1       2.7 23350 -4410.4
## - CAR             1       2.7 23350 -4410.4
## - PIT             1       2.7 23350 -4410.3
## - BUF             1       2.8 23350 -4410.3
## - DAL             1       3.0 23350 -4410.1
## - IND             1       3.0 23350 -4410.1
## - bad_weather_1   1       3.0 23350 -4410.0
## - CHI             1       3.7 23351 -4409.2
## - ATL             1       4.3 23351 -4408.5
## - NOR             1       7.1 23354 -4405.2
## - avg_rectd_plyr  1    3959.9 27307  -107.7
## 
## Step:  AIC=-4413.3
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MIA + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - MIA             1       0.2 23347 -4415.1
## - PHI             1       0.2 23348 -4415.1
## - CLE             1       0.2 23348 -4415.0
## - NYJ             1       0.2 23348 -4415.0
## - ARI             1       0.2 23348 -4415.0
## - SEA             1       0.3 23348 -4415.0
## - hot_weather     1       0.6 23348 -4414.6
## - HOU             1       0.7 23348 -4414.5
## - grass_1         1       0.8 23348 -4414.3
## - NE              1       0.9 23348 -4414.2
## - BAL             1       1.0 23348 -4414.1
## - TB              1       1.1 23348 -4414.0
## - WAS             1       1.2 23348 -4413.9
## - DET             1       1.4 23349 -4413.6
## - JAC             1       1.7 23349 -4413.4
## - KC              1       1.7 23349 -4413.3
## - NYG             1       1.7 23349 -4413.3
## - OAK             1       1.7 23349 -4413.3
## <none>                        23347 -4413.3
## - DEN             1       1.7 23349 -4413.3
## - GB              1       1.8 23349 -4413.2
## - TEN             1       2.0 23349 -4412.9
## - CIN             1       2.1 23349 -4412.9
## - SD              1       2.5 23350 -4412.4
## - CAR             1       2.5 23350 -4412.4
## - PIT             1       2.5 23350 -4412.3
## - BUF             1       2.6 23350 -4412.3
## - home_team_1     1       2.7 23350 -4412.1
## - DAL             1       2.7 23350 -4412.1
## - IND             1       2.8 23350 -4412.1
## - bad_weather_1   1       3.0 23350 -4411.8
## - CHI             1       3.5 23351 -4411.2
## - ATL             1       4.1 23351 -4410.4
## - NOR             1       7.1 23354 -4407.0
## - avg_rectd_plyr  1    3960.1 27307  -109.2
## 
## Step:  AIC=-4415.11
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - PHI             1       0.1 23348 -4417.0
## - CLE             1       0.2 23348 -4416.9
## - NYJ             1       0.2 23348 -4416.9
## - ARI             1       0.2 23348 -4416.9
## - SEA             1       0.2 23348 -4416.9
## - HOU             1       0.5 23348 -4416.5
## - hot_weather     1       0.6 23348 -4416.4
## - grass_1         1       0.8 23348 -4416.2
## - NE              1       0.8 23348 -4416.2
## - BAL             1       0.9 23348 -4416.1
## - TB              1       0.9 23348 -4416.0
## - WAS             1       1.0 23348 -4415.9
## - DET             1       1.3 23349 -4415.6
## - JAC             1       1.5 23349 -4415.3
## - KC              1       1.5 23349 -4415.3
## - NYG             1       1.5 23349 -4415.3
## - OAK             1       1.5 23349 -4415.3
## - DEN             1       1.6 23349 -4415.3
## - GB              1       1.7 23349 -4415.2
## <none>                        23347 -4415.1
## - TEN             1       1.9 23349 -4414.9
## - CIN             1       1.9 23349 -4414.9
## - SD              1       2.3 23350 -4414.4
## - CAR             1       2.3 23350 -4414.4
## - PIT             1       2.4 23350 -4414.3
## - BUF             1       2.4 23350 -4414.3
## - DAL             1       2.6 23350 -4414.1
## - IND             1       2.6 23350 -4414.1
## - home_team_1     1       2.8 23350 -4413.8
## - bad_weather_1   1       3.0 23350 -4413.6
## - CHI             1       3.3 23351 -4413.2
## - ATL             1       4.0 23351 -4412.4
## - NOR             1       7.0 23354 -4408.9
## - avg_rectd_plyr  1    3962.7 27310  -108.4
## 
## Step:  AIC=-4416.98
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + NE + NOR + NYG + NYJ + OAK + PIT + SD + SEA + TB + TEN + 
##     WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - CLE             1       0.1 23348 -4418.8
## - NYJ             1       0.1 23348 -4418.8
## - ARI             1       0.1 23348 -4418.8
## - SEA             1       0.1 23348 -4418.8
## - HOU             1       0.5 23348 -4418.4
## - hot_weather     1       0.6 23348 -4418.2
## - NE              1       0.7 23348 -4418.1
## - grass_1         1       0.8 23348 -4418.1
## - BAL             1       0.8 23348 -4418.1
## - TB              1       0.9 23348 -4418.0
## - WAS             1       0.9 23349 -4417.9
## - DET             1       1.2 23349 -4417.6
## - JAC             1       1.4 23349 -4417.3
## - KC              1       1.4 23349 -4417.3
## - NYG             1       1.4 23349 -4417.3
## - OAK             1       1.4 23349 -4417.3
## - DEN             1       1.5 23349 -4417.3
## - GB              1       1.6 23349 -4417.1
## <none>                        23348 -4417.0
## - TEN             1       1.8 23349 -4416.9
## - CIN             1       1.8 23349 -4416.9
## - SD              1       2.2 23350 -4416.4
## - CAR             1       2.2 23350 -4416.4
## - PIT             1       2.2 23350 -4416.3
## - BUF             1       2.3 23350 -4416.3
## - DAL             1       2.5 23350 -4416.1
## - IND             1       2.5 23350 -4416.1
## - home_team_1     1       2.8 23350 -4415.7
## - bad_weather_1   1       3.0 23351 -4415.4
## - CHI             1       3.2 23351 -4415.2
## - ATL             1       3.9 23351 -4414.4
## - NOR             1       6.9 23355 -4410.8
## - avg_rectd_plyr  1    3965.2 27313  -107.8
## 
## Step:  AIC=-4418.85
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     NE + NOR + NYG + NYJ + OAK + PIT + SD + SEA + TB + TEN + 
##     WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - NYJ             1       0.1 23348 -4420.8
## - ARI             1       0.1 23348 -4420.7
## - SEA             1       0.1 23348 -4420.7
## - HOU             1       0.4 23348 -4420.4
## - hot_weather     1       0.6 23348 -4420.1
## - NE              1       0.6 23348 -4420.1
## - BAL             1       0.7 23348 -4420.0
## - grass_1         1       0.7 23348 -4420.0
## - TB              1       0.8 23348 -4419.9
## - WAS             1       0.8 23349 -4419.9
## - DET             1       1.1 23349 -4419.6
## - KC              1       1.3 23349 -4419.3
## - JAC             1       1.3 23349 -4419.3
## - NYG             1       1.3 23349 -4419.3
## - OAK             1       1.3 23349 -4419.3
## - DEN             1       1.4 23349 -4419.2
## - GB              1       1.5 23349 -4419.1
## - TEN             1       1.7 23349 -4418.9
## <none>                        23348 -4418.8
## - CIN             1       1.7 23349 -4418.8
## - SD              1       2.1 23350 -4418.4
## - CAR             1       2.1 23350 -4418.3
## - PIT             1       2.1 23350 -4418.3
## - BUF             1       2.2 23350 -4418.2
## - DAL             1       2.4 23350 -4418.1
## - IND             1       2.4 23350 -4418.0
## - home_team_1     1       2.8 23351 -4417.5
## - bad_weather_1   1       3.1 23351 -4417.3
## - CHI             1       3.1 23351 -4417.2
## - ATL             1       3.8 23351 -4416.4
## - NOR             1       6.8 23355 -4412.8
## - avg_rectd_plyr  1    3967.5 27315  -107.3
## 
## Step:  AIC=-4420.75
## tdrec ~ hot_weather + home_team_1 + ARI + ATL + BAL + BUF + CAR + 
##     CHI + CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     NE + NOR + NYG + OAK + PIT + SD + SEA + TB + TEN + WAS + 
##     avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - ARI             1       0.1 23348 -4422.7
## - SEA             1       0.1 23348 -4422.7
## - HOU             1       0.4 23348 -4422.3
## - NE              1       0.6 23348 -4422.1
## - hot_weather     1       0.6 23348 -4422.0
## - BAL             1       0.6 23348 -4422.0
## - TB              1       0.7 23349 -4421.9
## - WAS             1       0.8 23349 -4421.8
## - grass_1         1       0.8 23349 -4421.8
## - DET             1       1.0 23349 -4421.5
## - KC              1       1.2 23349 -4421.3
## - JAC             1       1.2 23349 -4421.3
## - NYG             1       1.2 23349 -4421.3
## - OAK             1       1.3 23349 -4421.3
## - DEN             1       1.3 23349 -4421.2
## - GB              1       1.4 23349 -4421.1
## - TEN             1       1.6 23349 -4420.9
## - CIN             1       1.6 23349 -4420.8
## <none>                        23348 -4420.8
## - SD              1       2.0 23350 -4420.4
## - CAR             1       2.0 23350 -4420.3
## - PIT             1       2.1 23350 -4420.3
## - BUF             1       2.1 23350 -4420.2
## - DAL             1       2.3 23350 -4420.1
## - IND             1       2.3 23350 -4420.0
## - home_team_1     1       2.9 23351 -4419.4
## - CHI             1       3.0 23351 -4419.2
## - bad_weather_1   1       3.1 23351 -4419.1
## - ATL             1       3.7 23351 -4418.4
## - NOR             1       6.8 23355 -4414.8
## - avg_rectd_plyr  1    3967.5 27315  -109.2
## 
## Step:  AIC=-4422.67
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI + 
##     CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC + NE + 
##     NOR + NYG + OAK + PIT + SD + SEA + TB + TEN + WAS + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - SEA             1       0.1 23348 -4424.6
## - HOU             1       0.3 23348 -4424.3
## - NE              1       0.5 23348 -4424.0
## - BAL             1       0.6 23348 -4424.0
## - hot_weather     1       0.6 23348 -4423.9
## - TB              1       0.7 23349 -4423.9
## - WAS             1       0.7 23349 -4423.8
## - grass_1         1       0.8 23349 -4423.7
## - DET             1       1.0 23349 -4423.5
## - KC              1       1.2 23349 -4423.3
## - JAC             1       1.2 23349 -4423.3
## - NYG             1       1.2 23349 -4423.3
## - OAK             1       1.2 23349 -4423.2
## - DEN             1       1.2 23349 -4423.2
## - GB              1       1.3 23349 -4423.1
## - TEN             1       1.5 23349 -4422.9
## - CIN             1       1.6 23349 -4422.8
## <none>                        23348 -4422.7
## - SD              1       2.0 23350 -4422.4
## - CAR             1       2.0 23350 -4422.3
## - PIT             1       2.0 23350 -4422.3
## - BUF             1       2.1 23350 -4422.2
## - DAL             1       2.2 23350 -4422.1
## - IND             1       2.2 23350 -4422.0
## - home_team_1     1       2.8 23351 -4421.4
## - CHI             1       2.9 23351 -4421.2
## - bad_weather_1   1       3.1 23351 -4421.1
## - ATL             1       3.6 23351 -4420.4
## - NOR             1       6.7 23355 -4416.8
## - avg_rectd_plyr  1    3968.0 27316  -110.7
## 
## Step:  AIC=-4424.6
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI + 
##     CIN + DAL + DEN + DET + GB + HOU + IND + JAC + KC + NE + 
##     NOR + NYG + OAK + PIT + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - HOU             1       0.3 23348 -4426.3
## - NE              1       0.5 23348 -4426.0
## - BAL             1       0.6 23348 -4425.9
## - hot_weather     1       0.6 23349 -4425.9
## - TB              1       0.6 23349 -4425.8
## - WAS             1       0.7 23349 -4425.8
## - grass_1         1       0.9 23349 -4425.6
## - DET             1       0.9 23349 -4425.5
## - KC              1       1.1 23349 -4425.3
## - NYG             1       1.1 23349 -4425.3
## - JAC             1       1.1 23349 -4425.3
## - OAK             1       1.2 23349 -4425.2
## - DEN             1       1.2 23349 -4425.2
## - GB              1       1.3 23349 -4425.1
## - TEN             1       1.5 23349 -4424.9
## - CIN             1       1.5 23349 -4424.8
## <none>                        23348 -4424.6
## - SD              1       1.9 23350 -4424.3
## - CAR             1       1.9 23350 -4424.3
## - PIT             1       2.0 23350 -4424.3
## - BUF             1       2.0 23350 -4424.2
## - DAL             1       2.2 23350 -4424.1
## - IND             1       2.2 23350 -4424.0
## - home_team_1     1       2.9 23351 -4423.2
## - CHI             1       2.9 23351 -4423.2
## - bad_weather_1   1       3.1 23351 -4423.0
## - ATL             1       3.5 23351 -4422.4
## - NOR             1       6.6 23355 -4418.8
## - avg_rectd_plyr  1    3971.0 27319  -109.6
## 
## Step:  AIC=-4426.25
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI + 
##     CIN + DAL + DEN + DET + GB + IND + JAC + KC + NE + NOR + 
##     NYG + OAK + PIT + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - NE              1       0.4 23349 -4427.7
## - BAL             1       0.5 23349 -4427.7
## - TB              1       0.6 23349 -4427.6
## - hot_weather     1       0.6 23349 -4427.5
## - WAS             1       0.6 23349 -4427.5
## - DET             1       0.8 23349 -4427.3
## - grass_1         1       0.9 23349 -4427.2
## - NYG             1       1.0 23349 -4427.0
## - KC              1       1.0 23349 -4427.0
## - JAC             1       1.1 23349 -4427.0
## - OAK             1       1.1 23349 -4427.0
## - DEN             1       1.1 23349 -4427.0
## - GB              1       1.2 23349 -4426.9
## - TEN             1       1.4 23350 -4426.6
## - CIN             1       1.4 23350 -4426.6
## <none>                        23348 -4426.3
## - SD              1       1.8 23350 -4426.1
## - CAR             1       1.8 23350 -4426.1
## - PIT             1       1.8 23350 -4426.1
## - BUF             1       1.9 23350 -4426.0
## - DAL             1       2.0 23350 -4425.9
## - IND             1       2.0 23350 -4425.9
## - home_team_1     1       2.7 23351 -4425.1
## - CHI             1       2.7 23351 -4425.0
## - bad_weather_1   1       3.1 23351 -4424.6
## - ATL             1       3.4 23352 -4424.3
## - NOR             1       6.4 23355 -4420.7
## - avg_rectd_plyr  1    3970.9 27319  -111.5
## 
## Step:  AIC=-4427.74
## tdrec ~ hot_weather + home_team_1 + ATL + BAL + BUF + CAR + CHI + 
##     CIN + DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + 
##     OAK + PIT + SD + TB + TEN + WAS + avg_rectd_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - BAL             1       0.4 23349 -4429.3
## - TB              1       0.5 23349 -4429.2
## - WAS             1       0.5 23349 -4429.1
## - hot_weather     1       0.6 23349 -4429.0
## - DET             1       0.7 23349 -4428.9
## - NYG             1       0.9 23350 -4428.7
## - KC              1       0.9 23350 -4428.6
## - JAC             1       0.9 23350 -4428.6
## - OAK             1       1.0 23350 -4428.6
## - DEN             1       1.0 23350 -4428.6
## - grass_1         1       1.0 23350 -4428.5
## - GB              1       1.0 23350 -4428.5
## - TEN             1       1.3 23350 -4428.3
## - CIN             1       1.3 23350 -4428.3
## - SD              1       1.7 23350 -4427.8
## - CAR             1       1.7 23350 -4427.8
## - PIT             1       1.7 23350 -4427.8
## <none>                        23349 -4427.7
## - BUF             1       1.7 23350 -4427.7
## - DAL             1       1.8 23350 -4427.6
## - IND             1       1.9 23351 -4427.5
## - CHI             1       2.6 23351 -4426.7
## - home_team_1     1       2.9 23352 -4426.4
## - ATL             1       3.2 23352 -4426.0
## - bad_weather_1   1       3.2 23352 -4426.0
## - NOR             1       6.1 23355 -4422.5
## - avg_rectd_plyr  1    4003.8 27352   -80.0
## 
## Step:  AIC=-4429.27
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + OAK + 
##     PIT + SD + TB + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - TB              1       0.4 23349 -4430.8
## - WAS             1       0.5 23350 -4430.7
## - hot_weather     1       0.6 23350 -4430.5
## - DET             1       0.6 23350 -4430.5
## - NYG             1       0.8 23350 -4430.3
## - KC              1       0.8 23350 -4430.3
## - JAC             1       0.9 23350 -4430.3
## - OAK             1       0.9 23350 -4430.3
## - DEN             1       0.9 23350 -4430.2
## - GB              1       0.9 23350 -4430.2
## - grass_1         1       1.1 23350 -4430.0
## - TEN             1       1.1 23350 -4429.9
## - CIN             1       1.1 23350 -4429.9
## - SD              1       1.5 23351 -4429.5
## - CAR             1       1.6 23351 -4429.4
## - PIT             1       1.6 23351 -4429.4
## - BUF             1       1.6 23351 -4429.4
## <none>                        23349 -4429.3
## - DAL             1       1.7 23351 -4429.3
## - IND             1       1.7 23351 -4429.2
## - CHI             1       2.4 23351 -4428.4
## - home_team_1     1       3.0 23352 -4427.8
## - ATL             1       3.0 23352 -4427.7
## - bad_weather_1   1       3.2 23352 -4427.6
## - NOR             1       5.9 23355 -4424.3
## - avg_rectd_plyr  1    4003.5 27353   -81.8
## 
## Step:  AIC=-4430.78
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + OAK + 
##     PIT + SD + TEN + WAS + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - WAS             1       0.4 23350 -4432.3
## - DET             1       0.6 23350 -4432.1
## - hot_weather     1       0.6 23350 -4432.1
## - NYG             1       0.7 23350 -4431.9
## - KC              1       0.8 23350 -4431.9
## - JAC             1       0.8 23350 -4431.9
## - OAK             1       0.8 23350 -4431.9
## - DEN             1       0.8 23350 -4431.9
## - GB              1       0.8 23350 -4431.8
## - grass_1         1       1.0 23350 -4431.7
## - TEN             1       1.0 23350 -4431.6
## - CIN             1       1.1 23351 -4431.5
## - SD              1       1.4 23351 -4431.1
## - CAR             1       1.4 23351 -4431.1
## - PIT             1       1.4 23351 -4431.1
## - BUF             1       1.5 23351 -4431.0
## - DAL             1       1.6 23351 -4430.9
## - IND             1       1.6 23351 -4430.8
## <none>                        23349 -4430.8
## - CHI             1       2.3 23352 -4430.1
## - ATL             1       2.9 23352 -4429.4
## - home_team_1     1       3.1 23353 -4429.2
## - bad_weather_1   1       3.1 23353 -4429.1
## - NOR             1       5.7 23355 -4426.1
## - avg_rectd_plyr  1    4003.5 27353   -83.4
## 
## Step:  AIC=-4432.32
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + DET + GB + IND + JAC + KC + NOR + NYG + OAK + 
##     PIT + SD + TEN + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - DET             1       0.5 23350 -4433.7
## - hot_weather     1       0.6 23350 -4433.6
## - KC              1       0.7 23351 -4433.5
## - NYG             1       0.7 23351 -4433.5
## - OAK             1       0.7 23351 -4433.5
## - JAC             1       0.7 23351 -4433.5
## - DEN             1       0.7 23351 -4433.5
## - GB              1       0.8 23351 -4433.4
## - grass_1         1       0.8 23351 -4433.3
## - TEN             1       0.9 23351 -4433.2
## - CIN             1       1.0 23351 -4433.2
## - SD              1       1.3 23351 -4432.8
## - CAR             1       1.3 23351 -4432.8
## - PIT             1       1.3 23351 -4432.8
## - BUF             1       1.4 23351 -4432.7
## - DAL             1       1.5 23351 -4432.5
## - IND             1       1.5 23351 -4432.5
## <none>                        23350 -4432.3
## - CHI             1       2.1 23352 -4431.8
## - ATL             1       2.7 23353 -4431.1
## - bad_weather_1   1       3.1 23353 -4430.7
## - home_team_1     1       3.1 23353 -4430.6
## - NOR             1       5.5 23355 -4427.8
## - avg_rectd_plyr  1    4003.3 27353   -85.2
## 
## Step:  AIC=-4433.7
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + GB + IND + JAC + KC + NOR + NYG + OAK + PIT + 
##     SD + TEN + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - NYG             1       0.6 23351 -4435.0
## - KC              1       0.6 23351 -4435.0
## - OAK             1       0.6 23351 -4435.0
## - JAC             1       0.6 23351 -4435.0
## - hot_weather     1       0.6 23351 -4435.0
## - DEN             1       0.6 23351 -4435.0
## - GB              1       0.7 23351 -4434.9
## - TEN             1       0.9 23351 -4434.7
## - CIN             1       0.9 23351 -4434.7
## - grass_1         1       0.9 23351 -4434.6
## - SD              1       1.2 23352 -4434.3
## - CAR             1       1.2 23352 -4434.3
## - PIT             1       1.2 23352 -4434.3
## - BUF             1       1.3 23352 -4434.2
## - DAL             1       1.4 23352 -4434.1
## - IND             1       1.4 23352 -4434.0
## <none>                        23350 -4433.7
## - CHI             1       2.0 23352 -4433.3
## - ATL             1       2.6 23353 -4432.7
## - home_team_1     1       3.0 23353 -4432.2
## - bad_weather_1   1       3.1 23353 -4432.1
## - NOR             1       5.3 23356 -4429.5
## - avg_rectd_plyr  1    4013.9 27364   -76.0
## 
## Step:  AIC=-4435
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + GB + IND + JAC + KC + NOR + OAK + PIT + SD + 
##     TEN + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - KC              1       0.5 23352 -4436.4
## - OAK             1       0.6 23352 -4436.4
## - JAC             1       0.6 23352 -4436.3
## - DEN             1       0.6 23352 -4436.3
## - GB              1       0.6 23352 -4436.3
## - hot_weather     1       0.6 23352 -4436.3
## - TEN             1       0.8 23352 -4436.1
## - CIN             1       0.8 23352 -4436.1
## - grass_1         1       1.0 23352 -4435.8
## - CAR             1       1.1 23352 -4435.7
## - PIT             1       1.1 23352 -4435.7
## - SD              1       1.1 23352 -4435.7
## - BUF             1       1.2 23352 -4435.6
## - DAL             1       1.3 23352 -4435.5
## - IND             1       1.3 23352 -4435.5
## <none>                        23351 -4435.0
## - CHI             1       1.9 23353 -4434.7
## - ATL             1       2.4 23353 -4434.1
## - home_team_1     1       3.1 23354 -4433.4
## - bad_weather_1   1       3.2 23354 -4433.3
## - NOR             1       5.1 23356 -4431.0
## - avg_rectd_plyr  1    4017.9 27369   -73.4
## 
## Step:  AIC=-4436.36
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + GB + IND + JAC + NOR + OAK + PIT + SD + TEN + 
##     avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - OAK             1       0.5 23352 -4437.8
## - JAC             1       0.5 23352 -4437.8
## - DEN             1       0.5 23352 -4437.8
## - GB              1       0.5 23352 -4437.7
## - hot_weather     1       0.7 23352 -4437.6
## - TEN             1       0.7 23352 -4437.5
## - CIN             1       0.7 23352 -4437.5
## - grass_1         1       0.9 23352 -4437.4
## - PIT             1       1.0 23353 -4437.2
## - CAR             1       1.0 23353 -4437.2
## - SD              1       1.0 23353 -4437.2
## - BUF             1       1.1 23353 -4437.1
## - DAL             1       1.2 23353 -4436.9
## - IND             1       1.2 23353 -4436.9
## <none>                        23352 -4436.4
## - CHI             1       1.8 23353 -4436.3
## - ATL             1       2.3 23354 -4435.6
## - home_team_1     1       3.1 23355 -4434.7
## - bad_weather_1   1       3.2 23355 -4434.6
## - NOR             1       4.9 23356 -4432.6
## - avg_rectd_plyr  1    4018.8 27370   -73.9
## 
## Step:  AIC=-4437.81
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + GB + IND + JAC + NOR + PIT + SD + TEN + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - JAC             1       0.4 23352 -4439.3
## - DEN             1       0.4 23352 -4439.3
## - GB              1       0.5 23352 -4439.3
## - TEN             1       0.6 23353 -4439.1
## - CIN             1       0.7 23353 -4439.0
## - hot_weather     1       0.7 23353 -4439.0
## - grass_1         1       0.7 23353 -4439.0
## - PIT             1       0.9 23353 -4438.7
## - SD              1       0.9 23353 -4438.7
## - CAR             1       0.9 23353 -4438.7
## - BUF             1       1.0 23353 -4438.6
## - DAL             1       1.2 23353 -4438.5
## - IND             1       1.2 23353 -4438.4
## - CHI             1       1.7 23354 -4437.8
## <none>                        23352 -4437.8
## - ATL             1       2.2 23354 -4437.2
## - home_team_1     1       3.1 23355 -4436.1
## - bad_weather_1   1       3.2 23355 -4436.1
## - NOR             1       4.8 23357 -4434.2
## - avg_rectd_plyr  1    4018.4 27370   -75.9
## 
## Step:  AIC=-4439.31
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + DEN + GB + IND + NOR + PIT + SD + TEN + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - DEN             1       0.4 23353 -4440.9
## - GB              1       0.4 23353 -4440.8
## - TEN             1       0.6 23353 -4440.6
## - CIN             1       0.6 23353 -4440.6
## - grass_1         1       0.6 23353 -4440.6
## - hot_weather     1       0.7 23353 -4440.5
## - PIT             1       0.9 23353 -4440.3
## - SD              1       0.9 23353 -4440.3
## - CAR             1       0.9 23353 -4440.3
## - BUF             1       1.0 23353 -4440.1
## - DAL             1       1.1 23354 -4440.0
## - IND             1       1.1 23354 -4440.0
## - CHI             1       1.6 23354 -4439.4
## <none>                        23352 -4439.3
## - ATL             1       2.2 23355 -4438.8
## - bad_weather_1   1       3.1 23356 -4437.6
## - home_team_1     1       3.2 23356 -4437.6
## - NOR             1       4.7 23357 -4435.8
## - avg_rectd_plyr  1    4018.0 27370   -77.8
## 
## Step:  AIC=-4440.87
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + GB + IND + NOR + PIT + SD + TEN + avg_rectd_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - GB              1       0.4 23353 -4442.4
## - TEN             1       0.5 23353 -4442.3
## - grass_1         1       0.6 23353 -4442.2
## - CIN             1       0.6 23353 -4442.2
## - hot_weather     1       0.7 23353 -4442.1
## - PIT             1       0.8 23354 -4441.9
## - SD              1       0.8 23354 -4441.9
## - CAR             1       0.8 23354 -4441.9
## - BUF             1       0.9 23354 -4441.8
## - DAL             1       1.0 23354 -4441.6
## - IND             1       1.1 23354 -4441.6
## - CHI             1       1.5 23354 -4441.1
## <none>                        23353 -4440.9
## - ATL             1       2.1 23355 -4440.4
## - bad_weather_1   1       3.1 23356 -4439.3
## - home_team_1     1       3.3 23356 -4439.0
## - NOR             1       4.6 23357 -4437.5
## - avg_rectd_plyr  1    4027.6 27380   -69.9
## 
## Step:  AIC=-4442.44
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + IND + NOR + PIT + SD + TEN + avg_rectd_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - TEN             1       0.5 23354 -4443.9
## - grass_1         1       0.5 23354 -4443.9
## - CIN             1       0.6 23354 -4443.8
## - hot_weather     1       0.7 23354 -4443.6
## - PIT             1       0.7 23354 -4443.6
## - SD              1       0.7 23354 -4443.6
## - CAR             1       0.8 23354 -4443.6
## - BUF             1       0.9 23354 -4443.4
## - DAL             1       1.0 23354 -4443.3
## - IND             1       1.0 23354 -4443.2
## - CHI             1       1.4 23355 -4442.7
## <none>                        23353 -4442.4
## - ATL             1       2.0 23355 -4442.1
## - bad_weather_1   1       3.1 23356 -4440.7
## - home_team_1     1       3.3 23356 -4440.6
## - NOR             1       4.5 23358 -4439.2
## - avg_rectd_plyr  1    4060.9 27414   -38.1
## 
## Step:  AIC=-4443.88
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + IND + NOR + PIT + SD + avg_rectd_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - grass_1         1       0.4 23354 -4445.4
## - CIN             1       0.5 23354 -4445.3
## - PIT             1       0.7 23354 -4445.1
## - SD              1       0.7 23354 -4445.1
## - CAR             1       0.7 23354 -4445.1
## - hot_weather     1       0.7 23354 -4445.0
## - BUF             1       0.8 23354 -4444.9
## - DAL             1       1.0 23355 -4444.8
## - IND             1       1.0 23355 -4444.7
## - CHI             1       1.4 23355 -4444.3
## <none>                        23354 -4443.9
## - ATL             1       2.0 23356 -4443.6
## - bad_weather_1   1       3.0 23357 -4442.3
## - home_team_1     1       3.3 23357 -4442.0
## - NOR             1       4.4 23358 -4440.7
## - avg_rectd_plyr  1    4060.9 27415   -39.6
## 
## Step:  AIC=-4445.39
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + IND + NOR + PIT + SD + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - SD              1       0.6 23355 -4446.7
## - PIT             1       0.6 23355 -4446.7
## - CIN             1       0.6 23355 -4446.7
## - CAR             1       0.6 23355 -4446.6
## - hot_weather     1       0.8 23355 -4446.5
## - BUF             1       1.0 23355 -4446.2
## - DAL             1       1.1 23355 -4446.2
## - IND             1       1.1 23355 -4446.1
## - CHI             1       1.3 23355 -4445.9
## <none>                        23354 -4445.4
## - ATL             1       2.1 23356 -4444.9
## - bad_weather_1   1       3.0 23357 -4443.9
## - home_team_1     1       3.0 23357 -4443.8
## - NOR             1       4.6 23359 -4441.9
## - avg_rectd_plyr  1    4061.6 27416   -40.5
## 
## Step:  AIC=-4446.69
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + IND + NOR + PIT + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - PIT             1       0.5 23355 -4448.0
## - CIN             1       0.6 23355 -4448.0
## - CAR             1       0.6 23355 -4448.0
## - hot_weather     1       0.7 23355 -4447.8
## - BUF             1       0.9 23356 -4447.6
## - DAL             1       1.0 23356 -4447.5
## - IND             1       1.0 23356 -4447.5
## - CHI             1       1.2 23356 -4447.3
## <none>                        23355 -4446.7
## - ATL             1       2.0 23357 -4446.3
## - bad_weather_1   1       2.9 23358 -4445.2
## - home_team_1     1       3.1 23358 -4445.1
## - NOR             1       4.5 23359 -4443.4
## - avg_rectd_plyr  1    4065.9 27421   -37.6
## 
## Step:  AIC=-4448.04
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + CIN + 
##     DAL + IND + NOR + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - CIN             1       0.5 23356 -4449.4
## - CAR             1       0.5 23356 -4449.4
## - hot_weather     1       0.7 23356 -4449.2
## - BUF             1       0.9 23356 -4449.0
## - DAL             1       0.9 23356 -4448.9
## - IND             1       1.0 23356 -4448.9
## - CHI             1       1.1 23356 -4448.7
## <none>                        23355 -4448.0
## - ATL             1       1.9 23357 -4447.8
## - bad_weather_1   1       3.0 23358 -4446.5
## - home_team_1     1       3.2 23358 -4446.3
## - NOR             1       4.4 23360 -4444.9
## - avg_rectd_plyr  1    4068.9 27424   -36.0
## 
## Step:  AIC=-4449.42
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CAR + CHI + DAL + 
##     IND + NOR + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - CAR             1       0.5 23356 -4450.8
## - hot_weather     1       0.7 23356 -4450.6
## - BUF             1       0.8 23357 -4450.5
## - DAL             1       0.9 23357 -4450.4
## - IND             1       0.9 23357 -4450.3
## - CHI             1       1.1 23357 -4450.1
## <none>                        23356 -4449.4
## - ATL             1       1.9 23358 -4449.2
## - bad_weather_1   1       3.0 23359 -4447.8
## - home_team_1     1       3.2 23359 -4447.6
## - NOR             1       4.3 23360 -4446.4
## - avg_rectd_plyr  1    4068.4 27424   -38.0
## 
## Step:  AIC=-4450.84
## tdrec ~ hot_weather + home_team_1 + ATL + BUF + CHI + DAL + IND + 
##     NOR + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - hot_weather     1       0.7 23357 -4452.0
## - BUF             1       0.8 23357 -4451.9
## - DAL             1       0.8 23357 -4451.8
## - IND             1       0.9 23357 -4451.8
## - CHI             1       1.0 23357 -4451.6
## <none>                        23356 -4450.8
## - ATL             1       1.8 23358 -4450.7
## - bad_weather_1   1       3.0 23359 -4449.3
## - home_team_1     1       3.3 23359 -4449.0
## - NOR             1       4.2 23360 -4447.9
## - avg_rectd_plyr  1    4067.9 27424   -40.0
## 
## Step:  AIC=-4451.97
## tdrec ~ home_team_1 + ATL + BUF + CHI + DAL + IND + NOR + avg_rectd_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - BUF             1       0.7 23358 -4453.1
## - DAL             1       0.9 23358 -4453.0
## - IND             1       0.9 23358 -4452.9
## - CHI             1       1.0 23358 -4452.7
## <none>                        23357 -4452.0
## - ATL             1       1.8 23359 -4451.8
## - bad_weather_1   1       3.1 23360 -4450.3
## - home_team_1     1       3.3 23360 -4450.1
## - NOR             1       4.1 23361 -4449.1
## - avg_rectd_plyr  1    4067.6 27425   -41.5
## 
## Step:  AIC=-4453.11
## tdrec ~ home_team_1 + ATL + CHI + DAL + IND + NOR + avg_rectd_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - DAL             1       0.8 23358 -4454.2
## - IND             1       0.8 23359 -4454.1
## - CHI             1       1.0 23359 -4453.9
## <none>                        23358 -4453.1
## - ATL             1       1.7 23359 -4453.1
## - bad_weather_1   1       3.1 23361 -4451.4
## - home_team_1     1       3.3 23361 -4451.2
## - NOR             1       4.0 23362 -4450.4
## - avg_rectd_plyr  1    4067.0 27425   -43.5
## 
## Step:  AIC=-4454.15
## tdrec ~ home_team_1 + ATL + CHI + IND + NOR + avg_rectd_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - IND             1       0.8 23359 -4455.3
## - CHI             1       0.9 23359 -4455.1
## - ATL             1       1.6 23360 -4454.3
## <none>                        23358 -4454.2
## - home_team_1     1       2.9 23361 -4452.7
## - bad_weather_1   1       3.1 23362 -4452.5
## - NOR             1       3.8 23362 -4451.7
## - avg_rectd_plyr  1    4077.6 27436   -34.0
## 
## Step:  AIC=-4455.27
## tdrec ~ home_team_1 + ATL + CHI + NOR + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - CHI             1       0.9 23360 -4456.2
## - ATL             1       1.5 23361 -4455.5
## <none>                        23359 -4455.3
## - home_team_1     1       2.6 23362 -4454.2
## - bad_weather_1   1       3.1 23362 -4453.6
## - NOR             1       3.7 23363 -4452.9
## - avg_rectd_plyr  1    4080.3 27439   -32.6
## 
## Step:  AIC=-4456.23
## tdrec ~ home_team_1 + ATL + NOR + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - ATL             1       1.4 23362 -4456.5
## <none>                        23360 -4456.2
## - home_team_1     1       2.7 23363 -4455.0
## - bad_weather_1   1       3.2 23363 -4454.4
## - NOR             1       3.6 23364 -4454.0
## - avg_rectd_plyr  1    4079.7 27440   -34.3
## 
## Step:  AIC=-4456.53
## tdrec ~ home_team_1 + NOR + avg_rectd_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## <none>                        23362 -4456.5
## - home_team_1     1       2.3 23364 -4455.9
## - bad_weather_1   1       3.1 23365 -4454.8
## - NOR             1       3.4 23365 -4454.6
## - avg_rectd_plyr  1    4087.2 27449   -27.3

Passing

Passing Yards

PreProcess:

set.seed(123)
splitpy <- sample.split(nfl_data$py, SplitRatio = 0.7)
Trainpy <- subset(nfl_data, split == TRUE)
Testpy <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainpy, method = c("center", "scale"))
trainTransformedpy <- predict(preProcValues, Trainpy)
testTransformedpy <- predict(preProcValues, Testpy)

ggpairs:

ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("py",colnames(filtered_nfl_data_fields[46:51]))])

Regression:

pyregform <- formula(paste("py ~ ", 
                              paste(colnames(filtered_nfl_data_fields), collapse="+")))


linRegQBpyds <- lm(pyregform, data = trainTransformedpy)

summary(linRegQBpyds)
## 
## Call:
## lm(formula = pyregform, data = trainTransformedpy)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0235 -0.0522 -0.0126  0.0295  4.9218 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      1.296e-15  2.338e-03   0.000 1.000000    
## height           4.426e-02  4.537e-03   9.756  < 2e-16 ***
## weight          -2.624e-02  4.252e-03  -6.170 6.93e-10 ***
## cold_weather    -7.137e-03  2.462e-03  -2.900 0.003740 ** 
## hot_weather     -2.222e-03  2.360e-03  -0.941 0.346472    
## home_team_1      2.547e-03  2.544e-03   1.001 0.316727    
## forty1           1.476e-02  4.036e-03   3.657 0.000256 ***
## vertical1       -1.170e-02  3.103e-03  -3.772 0.000162 ***
## ARI             -6.302e-04  3.271e-03  -0.193 0.847232    
## ATL             -5.329e-03  3.287e-03  -1.621 0.104973    
## BAL             -2.789e-03  3.290e-03  -0.848 0.396465    
## BUF             -2.859e-04  3.247e-03  -0.088 0.929834    
## CAR             -6.943e-04  3.226e-03  -0.215 0.829610    
## CHI             -5.189e-03  3.190e-03  -1.627 0.103848    
## CIN             -7.107e-03  3.249e-03  -2.187 0.028718 *  
## CLE              4.537e-03  3.234e-03   1.403 0.160610    
## DAL             -1.184e-02  3.267e-03  -3.623 0.000291 ***
## DEN             -5.007e-03  3.279e-03  -1.527 0.126763    
## DET             -3.076e-03  3.234e-03  -0.951 0.341491    
## GB              -1.887e-02  3.329e-03  -5.668 1.46e-08 ***
## HOU              5.940e-03  3.290e-03   1.806 0.070961 .  
## IND             -6.637e-03  3.266e-03  -2.032 0.042118 *  
## JAC             -2.851e-03  3.186e-03  -0.895 0.370848    
## KC               2.147e-03  3.255e-03   0.660 0.509512    
## MIA             -2.479e-03  3.203e-03  -0.774 0.438955    
## MINN             1.991e-03  3.223e-03   0.618 0.536695    
## NE              -1.560e-02  3.366e-03  -4.637 3.56e-06 ***
## NOR             -1.218e-02  3.355e-03  -3.631 0.000283 ***
## NYG             -9.752e-03  3.279e-03  -2.974 0.002946 ** 
## NYJ             -4.306e-03  3.267e-03  -1.318 0.187529    
## OAK             -4.814e-03  3.288e-03  -1.464 0.143206    
## PHI              5.844e-03  3.186e-03   1.834 0.066651 .  
## PIT             -1.521e-03  3.270e-03  -0.465 0.641843    
## SD              -1.145e-02  3.209e-03  -3.567 0.000361 ***
## SEA             -4.269e-04  3.330e-03  -0.128 0.897991    
## STL             -1.781e-03  3.241e-03  -0.550 0.582613    
## TB              -6.106e-03  3.211e-03  -1.902 0.057206 .  
## TEN             -3.634e-03  3.230e-03  -1.125 0.260596    
## WAS              5.401e-03  3.247e-03   1.663 0.096247 .  
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -1.591e-02  2.986e-03  -5.326 1.01e-07 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr   -2.445e-02  3.574e-03  -6.841 8.04e-12 ***
## avg_rbry_pos     1.339e-02  4.164e-03   3.216 0.001300 ** 
## avg_fuml_plyr    7.685e-02  3.454e-03  22.249  < 2e-16 ***
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr   8.464e-01  3.752e-03 225.574  < 2e-16 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -2.140e-03  2.690e-03  -0.795 0.426406    
## bad_weather_1   -5.485e-03  2.379e-03  -2.306 0.021139 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3877 on 27438 degrees of freedom
## Multiple R-squared:   0.85,  Adjusted R-squared:  0.8497 
## F-statistic:  3454 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegQBpyds2 <- update(linRegQBpyds, ~.-hot_weather-home_team_1-vertical1-ATL-BAL-DAL-DEN-DET-KC
                        -NOR-PHI-PIT-SEA-SD-WAS-avg_trg_team-avg_tdr_team-avg_rbra_team-avg_rbry_plyr
                        -avg_fuml_team-avg_qbints_team-avg_qbtdp_team-grass_1)

summary(linRegQBpyds2)
## 
## Call:
## lm(formula = py ~ height + weight + cold_weather + forty1 + ARI + 
##     BUF + CAR + CHI + CIN + CLE + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NYG + NYJ + OAK + STL + TB + TEN + avg_rectd_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1, 
##     data = trainTransformedpy)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0413 -0.0521 -0.0106  0.0261  4.9606 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.289e-15  2.344e-03   0.000 1.000000    
## height          4.148e-02  4.525e-03   9.166  < 2e-16 ***
## weight         -2.680e-02  4.230e-03  -6.336 2.40e-10 ***
## cold_weather   -5.096e-03  2.412e-03  -2.113 0.034614 *  
## forty1          2.488e-02  3.391e-03   7.338 2.23e-13 ***
## ARI             3.054e-03  2.400e-03   1.273 0.203163    
## BUF             3.269e-03  2.400e-03   1.362 0.173119    
## CAR             1.795e-03  2.397e-03   0.749 0.453945    
## CHI            -2.204e-03  2.401e-03  -0.918 0.358631    
## CIN            -4.019e-03  2.399e-03  -1.675 0.093918 .  
## CLE             7.153e-03  2.410e-03   2.968 0.003001 ** 
## GB             -1.565e-02  2.416e-03  -6.477 9.52e-11 ***
## HOU             8.488e-03  2.408e-03   3.525 0.000424 ***
## IND            -3.844e-03  2.395e-03  -1.605 0.108539    
## JAC            -4.243e-04  2.395e-03  -0.177 0.859370    
## MIA             1.151e-03  2.393e-03   0.481 0.630424    
## MINN            4.273e-03  2.405e-03   1.777 0.075588 .  
## NE             -1.233e-02  2.445e-03  -5.044 4.58e-07 ***
## NYG            -6.020e-03  2.400e-03  -2.508 0.012151 *  
## NYJ            -1.940e-03  2.399e-03  -0.809 0.418794    
## OAK            -9.088e-04  2.413e-03  -0.377 0.706470    
## STL             1.559e-03  2.404e-03   0.648 0.516748    
## TB             -2.803e-03  2.398e-03  -1.169 0.242444    
## TEN            -7.200e-04  2.401e-03  -0.300 0.764233    
## avg_rectd_plyr -1.931e-02  2.963e-03  -6.518 7.25e-11 ***
## avg_rbry_pos   -4.247e-03  3.477e-03  -1.221 0.221986    
## avg_fuml_plyr   7.115e-02  3.245e-03  21.926  < 2e-16 ***
## avg_qbtdp_plyr  8.484e-01  3.706e-03 228.891  < 2e-16 ***
## bad_weather_1  -5.277e-03  2.379e-03  -2.218 0.026589 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3885 on 27455 degrees of freedom
## Multiple R-squared:  0.8492, Adjusted R-squared:  0.849 
## F-statistic:  5521 on 28 and 27455 DF,  p-value: < 2.2e-16

This prediction actually turned out to be pretty strong (R2 0.87) and we did it with only 5 variables! This makes sense to me. QB is a 1 player position, with a significant investment in the player. A QB will get time to mature and prove himself good or bad.

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

PydsdPredicted <- predict(linRegQBpyds2, newdata = testTransformedpy)

SSEpyds <- sum((PydsdPredicted - testTransformedpy$py)^2)
SSTpyds <- sum((mean(nfl_data$py)-testTransformedpy$py)^2)
r2_pyds <- 1 - SSEpyds/SSTpyds 
r2_pyds
## [1] 0.999716
rmse_pyds <- sqrt(SSEpyds/nrow(testTransformedpy))
rmse_pyds
## [1] 0.4007825

Below are the regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBpyds2, which = c(1:3,5))

The normal Q-Q shows are data has extreme values, and means the data is probably not normally distributed

Some more summary statistics:

confint(linRegQBpyds2)
##                        2.5 %        97.5 %
## (Intercept)    -0.0045936970  0.0045936970
## height          0.0326078543  0.0503464791
## weight         -0.0350933025 -0.0185105021
## cold_weather   -0.0098236426 -0.0003687761
## forty1          0.0182347552  0.0315260322
## ARI            -0.0016498965  0.0077587289
## BUF            -0.0014345387  0.0079730819
## CAR            -0.0029037966  0.0064945761
## CHI            -0.0069102798  0.0025020177
## CIN            -0.0087219695  0.0006835929
## CLE             0.0024291162  0.0118777163
## GB             -0.0203876978 -0.0109148362
## HOU             0.0037682390  0.0132071276
## IND            -0.0085392589  0.0008508465
## JAC            -0.0051186886  0.0042700044
## MIA            -0.0035383674  0.0058406447
## MINN           -0.0004402949  0.0089861675
## NE             -0.0171234530 -0.0075402464
## NYG            -0.0107246243 -0.0013150442
## NYJ            -0.0066413585  0.0027623132
## OAK            -0.0056389235  0.0038212445
## STL            -0.0031534987  0.0062711114
## TB             -0.0075025120  0.0018969260
## TEN            -0.0054253315  0.0039853018
## avg_rectd_plyr -0.0251213934 -0.0135056939
## avg_rbry_pos   -0.0110621988  0.0025688193
## avg_fuml_plyr   0.0647915244  0.0775128589
## avg_qbtdp_plyr  0.8410944287  0.8556238723
## bad_weather_1  -0.0099402225 -0.0006128489
coef(summary(linRegQBpyds2))
##                     Estimate  Std. Error       t value      Pr(>|t|)
## (Intercept)     1.288901e-15 0.002343663  5.499515e-13  1.000000e+00
## height          4.147717e-02 0.004525043  9.166137e+00  5.235466e-20
## weight         -2.680190e-02 0.004230197 -6.335851e+00  2.396931e-10
## cold_weather   -5.096209e-03 0.002411894 -2.112949e+00  3.461410e-02
## forty1          2.488039e-02 0.003390545  7.338170e+00  2.225360e-13
## ARI             3.054416e-03 0.002400098  1.272622e+00  2.031631e-01
## BUF             3.269272e-03 0.002399842  1.362286e+00  1.731187e-01
## CAR             1.795390e-03 0.002397482  7.488646e-01  4.539452e-01
## CHI            -2.204131e-03 0.002401035 -9.179922e-01  3.586310e-01
## CIN            -4.019188e-03 0.002399316 -1.675139e+00  9.391838e-02
## CLE             7.153416e-03 0.002410295  2.967859e+00  3.001405e-03
## GB             -1.565127e-02 0.002416484 -6.476875e+00  9.522448e-11
## HOU             8.487683e-03 0.002407818  3.525052e+00  4.240887e-04
## IND            -3.844206e-03 0.002395373 -1.604846e+00  1.085391e-01
## JAC            -4.243421e-04 0.002395013 -1.771774e-01  8.593704e-01
## MIA             1.151139e-03 0.002392544  4.811359e-01  6.304237e-01
## MINN            4.272936e-03 0.002404648  1.776949e+00  7.558773e-02
## NE             -1.233185e-02 0.002444633 -5.044459e+00  4.577027e-07
## NYG            -6.019834e-03 0.002400341 -2.507908e+00  1.215057e-02
## NYJ            -1.939523e-03 0.002398834 -8.085272e-01  4.187942e-01
## OAK            -9.088395e-04 0.002413246 -3.766046e-01  7.064704e-01
## STL             1.558806e-03 0.002404175  6.483746e-01  5.167481e-01
## TB             -2.802793e-03 0.002397754 -1.168924e+00  2.424443e-01
## TEN            -7.200148e-04 0.002400610 -2.999299e-01  7.642329e-01
## avg_rectd_plyr -1.931354e-02 0.002963112 -6.517992e+00  7.248974e-11
## avg_rbry_pos   -4.246690e-03 0.003477211 -1.221292e+00  2.219860e-01
## avg_fuml_plyr   7.115219e-02 0.003245155  2.192567e+01 1.193963e-105
## avg_qbtdp_plyr  8.483592e-01 0.003706395  2.288906e+02  0.000000e+00
## bad_weather_1  -5.276536e-03 0.002379371 -2.217618e+00  2.658904e-02
anova(linRegQBpyds2)
## Analysis of Variance Table
## 
## Response: py
##                   Df Sum Sq Mean Sq    F value    Pr(>F)    
## height             1 1859.7  1859.7 12318.8750 < 2.2e-16 ***
## weight             1  446.2   446.2  2955.3921 < 2.2e-16 ***
## cold_weather       1    0.7     0.7     4.3623 0.0367522 *  
## forty1             1 5442.0  5442.0 36048.5596 < 2.2e-16 ***
## ARI                1    0.4     0.4     2.8024 0.0941360 .  
## BUF                1    0.5     0.5     3.6101 0.0574397 .  
## CAR                1   10.9    10.9    71.9797 < 2.2e-16 ***
## CHI                1    0.1     0.1     0.6070 0.4359401    
## CIN                1    4.2     4.2    27.8127 1.347e-07 ***
## CLE                1    1.9     1.9    12.7879 0.0003495 ***
## GB                 1    0.0     0.0     0.0314 0.8593892    
## HOU                1   15.1    15.1   100.2842 < 2.2e-16 ***
## IND                1   11.3    11.3    74.6888 < 2.2e-16 ***
## JAC                1    0.0     0.0     0.0713 0.7895004    
## MIA                1    0.6     0.6     3.8769 0.0489650 *  
## MINN               1    1.9     1.9    12.5342 0.0004002 ***
## NE                 1   34.2    34.2   226.3528 < 2.2e-16 ***
## NYG                1    7.3     7.3    48.0341 4.281e-12 ***
## NYJ                1    0.8     0.8     5.1984 0.0226151 *  
## OAK                1    0.1     0.1     0.9377 0.3328731    
## STL                1   26.8    26.8   177.4989 < 2.2e-16 ***
## TB                 1    3.2     3.2    20.8947 4.874e-06 ***
## TEN                1    5.7     5.7    38.0459 7.006e-10 ***
## avg_rectd_plyr     1 1872.3  1872.3 12402.0890 < 2.2e-16 ***
## avg_rbry_pos       1  311.0   311.0  2060.3374 < 2.2e-16 ***
## avg_fuml_plyr      1 5371.6  5371.6 35582.4880 < 2.2e-16 ***
## avg_qbtdp_plyr     1 7909.1  7909.1 52391.3106 < 2.2e-16 ***
## bad_weather_1      1    0.7     0.7     4.9178 0.0265890 *  
## Residuals      27455 4144.7     0.2                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_py <- step(lm(pyregform, data = trainTransformedpy), direction = "backward")
## Start:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52041.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BUF             1       0.0  4123.6 -52044
## - SEA             1       0.0  4123.6 -52044
## - ARI             1       0.0  4123.6 -52044
## - CAR             1       0.0  4123.6 -52044
## - PIT             1       0.0  4123.6 -52044
## - STL             1       0.0  4123.6 -52043
## - MINN            1       0.1  4123.7 -52043
## - KC              1       0.1  4123.7 -52043
## - MIA             1       0.1  4123.7 -52043
## - grass_1         1       0.1  4123.7 -52043
## - BAL             1       0.1  4123.7 -52043
## - JAC             1       0.1  4123.7 -52043
## - hot_weather     1       0.1  4123.7 -52043
## - DET             1       0.1  4123.7 -52043
## - home_team_1     1       0.2  4123.8 -52043
## - TEN             1       0.2  4123.8 -52042
## - NYJ             1       0.3  4123.9 -52042
## - CLE             1       0.3  4123.9 -52042
## <none>                         4123.6 -52042
## - OAK             1       0.3  4123.9 -52042
## - DEN             1       0.4  4124.0 -52041
## - ATL             1       0.4  4124.0 -52041
## - CHI             1       0.4  4124.0 -52041
## - WAS             1       0.4  4124.0 -52041
## - HOU             1       0.5  4124.1 -52040
## - PHI             1       0.5  4124.1 -52040
## - TB              1       0.5  4124.1 -52040
## - IND             1       0.6  4124.2 -52040
## - CIN             1       0.7  4124.3 -52039
## - bad_weather_1   1       0.8  4124.4 -52038
## - cold_weather    1       1.3  4124.9 -52035
## - NYG             1       1.3  4124.9 -52035
## - avg_rbry_pos    1       1.6  4125.2 -52033
## - SD              1       1.9  4125.5 -52031
## - DAL             1       2.0  4125.6 -52031
## - NOR             1       2.0  4125.6 -52031
## - forty1          1       2.0  4125.6 -52030
## - vertical1       1       2.1  4125.7 -52030
## - NE              1       3.2  4126.8 -52022
## - avg_rectd_plyr  1       4.3  4127.9 -52015
## - GB              1       4.8  4128.4 -52012
## - weight          1       5.7  4129.3 -52006
## - avg_rbry_plyr   1       7.0  4130.6 -51997
## - height          1      14.3  4137.9 -51949
## - avg_fuml_plyr   1      74.4  4198.0 -51552
## - avg_qbtdp_plyr  1    7647.2 11770.8 -23216
## 
## Step:  AIC=-52043.75
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - SEA             1       0.0  4123.6 -52046
## - ARI             1       0.0  4123.6 -52046
## - CAR             1       0.0  4123.6 -52046
## - PIT             1       0.0  4123.6 -52046
## - STL             1       0.1  4123.7 -52045
## - MINN            1       0.1  4123.7 -52045
## - grass_1         1       0.1  4123.7 -52045
## - KC              1       0.1  4123.7 -52045
## - MIA             1       0.1  4123.7 -52045
## - BAL             1       0.1  4123.7 -52045
## - hot_weather     1       0.1  4123.7 -52045
## - JAC             1       0.1  4123.7 -52045
## - home_team_1     1       0.2  4123.8 -52045
## - DET             1       0.2  4123.8 -52045
## - TEN             1       0.2  4123.8 -52044
## <none>                         4123.6 -52044
## - NYJ             1       0.3  4123.9 -52044
## - OAK             1       0.4  4124.0 -52043
## - CLE             1       0.4  4124.0 -52043
## - DEN             1       0.4  4124.0 -52043
## - CHI             1       0.5  4124.1 -52042
## - ATL             1       0.5  4124.1 -52042
## - WAS             1       0.6  4124.2 -52042
## - TB              1       0.7  4124.3 -52041
## - HOU             1       0.7  4124.3 -52041
## - PHI             1       0.7  4124.3 -52041
## - IND             1       0.8  4124.4 -52041
## - bad_weather_1   1       0.8  4124.4 -52040
## - CIN             1       0.9  4124.5 -52040
## - cold_weather    1       1.3  4124.9 -52037
## - avg_rbry_pos    1       1.6  4125.2 -52035
## - NYG             1       1.7  4125.3 -52034
## - forty1          1       2.0  4125.6 -52032
## - vertical1       1       2.1  4125.7 -52031
## - SD              1       2.4  4126.0 -52030
## - DAL             1       2.5  4126.1 -52029
## - NOR             1       2.6  4126.2 -52028
## - NE              1       4.2  4127.8 -52018
## - avg_rectd_plyr  1       4.3  4127.9 -52017
## - weight          1       5.7  4129.3 -52008
## - GB              1       6.3  4129.9 -52004
## - avg_rbry_plyr   1       7.0  4130.6 -51999
## - height          1      14.3  4137.9 -51950
## - avg_fuml_plyr   1      74.4  4198.0 -51554
## - avg_qbtdp_plyr  1    7651.6 11775.2 -23208
## 
## Step:  AIC=-52045.74
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - ARI             1       0.0  4123.6 -52048
## - CAR             1       0.0  4123.6 -52048
## - PIT             1       0.0  4123.6 -52048
## - STL             1       0.1  4123.7 -52047
## - grass_1         1       0.1  4123.7 -52047
## - MINN            1       0.1  4123.7 -52047
## - MIA             1       0.1  4123.7 -52047
## - KC              1       0.1  4123.7 -52047
## - hot_weather     1       0.1  4123.7 -52047
## - BAL             1       0.1  4123.7 -52047
## - JAC             1       0.1  4123.8 -52047
## - home_team_1     1       0.2  4123.8 -52047
## - DET             1       0.2  4123.8 -52047
## - TEN             1       0.2  4123.8 -52046
## <none>                         4123.6 -52046
## - NYJ             1       0.4  4124.0 -52045
## - OAK             1       0.4  4124.0 -52045
## - DEN             1       0.5  4124.1 -52045
## - CLE             1       0.5  4124.1 -52045
## - CHI             1       0.5  4124.1 -52044
## - ATL             1       0.5  4124.1 -52044
## - WAS             1       0.7  4124.3 -52043
## - TB              1       0.7  4124.3 -52043
## - PHI             1       0.8  4124.4 -52042
## - HOU             1       0.8  4124.4 -52042
## - bad_weather_1   1       0.8  4124.4 -52042
## - IND             1       0.9  4124.5 -52042
## - CIN             1       1.0  4124.6 -52041
## - cold_weather    1       1.3  4124.9 -52039
## - avg_rbry_pos    1       1.6  4125.2 -52037
## - NYG             1       1.9  4125.5 -52035
## - forty1          1       2.0  4125.6 -52034
## - vertical1       1       2.1  4125.7 -52033
## - SD              1       2.6  4126.2 -52030
## - DAL             1       2.8  4126.4 -52029
## - NOR             1       2.9  4126.5 -52028
## - avg_rectd_plyr  1       4.3  4127.9 -52019
## - NE              1       4.8  4128.4 -52016
## - weight          1       5.7  4129.3 -52010
## - avg_rbry_plyr   1       7.0  4130.6 -52001
## - GB              1       7.1  4130.7 -52001
## - height          1      14.4  4138.0 -51952
## - avg_fuml_plyr   1      74.6  4198.2 -51555
## - avg_qbtdp_plyr  1    7668.9 11792.5 -23169
## 
## Step:  AIC=-52047.72
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BAL + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - CAR             1       0.0  4123.6 -52050
## - PIT             1       0.0  4123.6 -52050
## - STL             1       0.0  4123.7 -52049
## - grass_1         1       0.1  4123.7 -52049
## - MIA             1       0.1  4123.7 -52049
## - MINN            1       0.1  4123.7 -52049
## - hot_weather     1       0.1  4123.7 -52049
## - KC              1       0.1  4123.7 -52049
## - BAL             1       0.1  4123.7 -52049
## - JAC             1       0.1  4123.8 -52049
## - home_team_1     1       0.2  4123.8 -52049
## - DET             1       0.2  4123.8 -52049
## - TEN             1       0.2  4123.9 -52048
## <none>                         4123.6 -52048
## - NYJ             1       0.4  4124.0 -52047
## - OAK             1       0.4  4124.0 -52047
## - DEN             1       0.5  4124.1 -52047
## - CLE             1       0.5  4124.1 -52046
## - CHI             1       0.5  4124.1 -52046
## - ATL             1       0.5  4124.2 -52046
## - WAS             1       0.7  4124.3 -52045
## - TB              1       0.8  4124.4 -52045
## - bad_weather_1   1       0.8  4124.4 -52044
## - PHI             1       0.9  4124.5 -52044
## - HOU             1       0.9  4124.5 -52044
## - IND             1       0.9  4124.5 -52044
## - CIN             1       1.0  4124.7 -52043
## - cold_weather    1       1.3  4124.9 -52041
## - avg_rbry_pos    1       1.6  4125.2 -52039
## - NYG             1       2.0  4125.6 -52036
## - forty1          1       2.0  4125.6 -52036
## - vertical1       1       2.1  4125.7 -52035
## - SD              1       2.7  4126.4 -52031
## - DAL             1       3.0  4126.6 -52030
## - NOR             1       3.1  4126.7 -52029
## - avg_rectd_plyr  1       4.3  4127.9 -52021
## - NE              1       5.0  4128.6 -52017
## - weight          1       5.7  4129.3 -52012
## - avg_rbry_plyr   1       7.0  4130.7 -52003
## - GB              1       7.4  4131.0 -52000
## - height          1      14.4  4138.0 -51954
## - avg_fuml_plyr   1      74.6  4198.2 -51557
## - avg_qbtdp_plyr  1    7675.3 11798.9 -23156
## 
## Step:  AIC=-52049.69
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - PIT             1       0.0  4123.6 -52052
## - STL             1       0.0  4123.7 -52051
## - grass_1         1       0.1  4123.7 -52051
## - MIA             1       0.1  4123.7 -52051
## - BAL             1       0.1  4123.7 -52051
## - hot_weather     1       0.1  4123.7 -52051
## - MINN            1       0.1  4123.7 -52051
## - JAC             1       0.1  4123.8 -52051
## - KC              1       0.2  4123.8 -52051
## - home_team_1     1       0.2  4123.8 -52051
## - DET             1       0.2  4123.8 -52051
## - TEN             1       0.2  4123.9 -52050
## <none>                         4123.6 -52050
## - NYJ             1       0.4  4124.0 -52049
## - OAK             1       0.4  4124.1 -52049
## - DEN             1       0.5  4124.1 -52048
## - CHI             1       0.5  4124.2 -52048
## - ATL             1       0.6  4124.2 -52048
## - CLE             1       0.6  4124.2 -52048
## - TB              1       0.8  4124.4 -52047
## - WAS             1       0.8  4124.4 -52046
## - bad_weather_1   1       0.8  4124.4 -52046
## - IND             1       0.9  4124.5 -52046
## - PHI             1       0.9  4124.5 -52046
## - HOU             1       0.9  4124.5 -52046
## - CIN             1       1.1  4124.7 -52045
## - cold_weather    1       1.3  4124.9 -52043
## - avg_rbry_pos    1       1.6  4125.2 -52041
## - forty1          1       2.0  4125.6 -52038
## - NYG             1       2.0  4125.6 -52038
## - vertical1       1       2.1  4125.8 -52037
## - SD              1       2.8  4126.4 -52033
## - DAL             1       3.0  4126.6 -52032
## - NOR             1       3.2  4126.8 -52031
## - avg_rectd_plyr  1       4.3  4127.9 -52023
## - NE              1       5.1  4128.7 -52018
## - weight          1       5.7  4129.4 -52013
## - avg_rbry_plyr   1       7.0  4130.7 -52005
## - GB              1       7.7  4131.3 -52000
## - height          1      14.4  4138.0 -51956
## - avg_fuml_plyr   1      74.6  4198.2 -51559
## - avg_qbtdp_plyr  1    7675.6 11799.2 -23158
## 
## Step:  AIC=-52051.5
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + SD + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - STL             1       0.0  4123.7 -52053
## - MIA             1       0.1  4123.7 -52053
## - grass_1         1       0.1  4123.8 -52053
## - BAL             1       0.1  4123.8 -52053
## - JAC             1       0.1  4123.8 -52053
## - hot_weather     1       0.1  4123.8 -52053
## - DET             1       0.2  4123.8 -52053
## - home_team_1     1       0.2  4123.8 -52052
## - MINN            1       0.2  4123.8 -52052
## - KC              1       0.2  4123.8 -52052
## - TEN             1       0.2  4123.9 -52052
## <none>                         4123.6 -52052
## - NYJ             1       0.3  4124.0 -52051
## - OAK             1       0.4  4124.1 -52051
## - DEN             1       0.5  4124.1 -52050
## - CHI             1       0.5  4124.2 -52050
## - ATL             1       0.5  4124.2 -52050
## - CLE             1       0.6  4124.3 -52049
## - TB              1       0.7  4124.4 -52049
## - bad_weather_1   1       0.8  4124.4 -52048
## - WAS             1       0.9  4124.5 -52048
## - IND             1       0.9  4124.5 -52048
## - HOU             1       1.0  4124.6 -52047
## - PHI             1       1.0  4124.6 -52047
## - CIN             1       1.0  4124.7 -52047
## - cold_weather    1       1.3  4125.0 -52045
## - avg_rbry_pos    1       1.6  4125.2 -52043
## - forty1          1       2.0  4125.7 -52040
## - NYG             1       2.0  4125.7 -52040
## - vertical1       1       2.1  4125.8 -52039
## - SD              1       2.8  4126.5 -52035
## - DAL             1       3.0  4126.7 -52033
## - NOR             1       3.1  4126.8 -52033
## - avg_rectd_plyr  1       4.3  4127.9 -52025
## - NE              1       5.1  4128.8 -52019
## - weight          1       5.7  4129.4 -52015
## - avg_rbry_plyr   1       7.0  4130.7 -52007
## - GB              1       7.8  4131.5 -52001
## - height          1      14.4  4138.0 -51958
## - avg_fuml_plyr   1      74.6  4198.2 -51561
## - avg_qbtdp_plyr  1    7676.5 11800.1 -23158
## 
## Step:  AIC=-52053.27
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - MIA             1       0.1  4123.8 -52055
## - BAL             1       0.1  4123.8 -52055
## - grass_1         1       0.1  4123.8 -52055
## - JAC             1       0.1  4123.8 -52055
## - DET             1       0.1  4123.8 -52054
## - hot_weather     1       0.1  4123.8 -52054
## - home_team_1     1       0.2  4123.8 -52054
## - MINN            1       0.2  4123.9 -52054
## - TEN             1       0.2  4123.9 -52054
## - KC              1       0.2  4123.9 -52054
## <none>                         4123.7 -52053
## - NYJ             1       0.3  4124.0 -52053
## - OAK             1       0.4  4124.1 -52053
## - DEN             1       0.4  4124.1 -52052
## - CHI             1       0.5  4124.2 -52052
## - ATL             1       0.5  4124.2 -52052
## - CLE             1       0.7  4124.4 -52051
## - TB              1       0.7  4124.4 -52051
## - bad_weather_1   1       0.8  4124.5 -52050
## - IND             1       0.8  4124.5 -52050
## - WAS             1       0.9  4124.6 -52049
## - CIN             1       1.0  4124.7 -52049
## - PHI             1       1.1  4124.7 -52048
## - HOU             1       1.1  4124.8 -52048
## - cold_weather    1       1.3  4125.0 -52047
## - avg_rbry_pos    1       1.6  4125.2 -52045
## - NYG             1       2.0  4125.7 -52042
## - forty1          1       2.0  4125.7 -52042
## - vertical1       1       2.1  4125.8 -52041
## - SD              1       2.8  4126.5 -52037
## - DAL             1       3.0  4126.7 -52035
## - NOR             1       3.1  4126.8 -52035
## - avg_rectd_plyr  1       4.3  4127.9 -52027
## - NE              1       5.1  4128.8 -52021
## - weight          1       5.7  4129.4 -52017
## - avg_rbry_plyr   1       7.0  4130.7 -52009
## - GB              1       7.8  4131.5 -52003
## - height          1      14.4  4138.0 -51960
## - avg_fuml_plyr   1      74.5  4198.2 -51563
## - avg_qbtdp_plyr  1    7700.6 11824.3 -23103
## 
## Step:  AIC=-52054.77
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BAL + CHI + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + KC + MINN + NE + NOR + 
##     NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BAL             1       0.1  4123.8 -52056
## - JAC             1       0.1  4123.8 -52056
## - DET             1       0.1  4123.9 -52056
## - grass_1         1       0.1  4123.9 -52056
## - hot_weather     1       0.1  4123.9 -52056
## - home_team_1     1       0.2  4123.9 -52056
## - TEN             1       0.2  4123.9 -52056
## - MINN            1       0.2  4124.0 -52055
## - KC              1       0.2  4124.0 -52055
## - NYJ             1       0.3  4124.0 -52055
## <none>                         4123.8 -52055
## - OAK             1       0.4  4124.1 -52054
## - DEN             1       0.4  4124.1 -52054
## - CHI             1       0.4  4124.2 -52054
## - ATL             1       0.5  4124.2 -52054
## - TB              1       0.7  4124.4 -52052
## - CLE             1       0.8  4124.5 -52052
## - bad_weather_1   1       0.8  4124.5 -52052
## - IND             1       0.8  4124.6 -52051
## - CIN             1       0.9  4124.7 -52050
## - WAS             1       1.0  4124.8 -52050
## - PHI             1       1.2  4124.9 -52049
## - HOU             1       1.2  4124.9 -52049
## - cold_weather    1       1.3  4125.0 -52048
## - avg_rbry_pos    1       1.5  4125.3 -52047
## - NYG             1       1.9  4125.7 -52044
## - forty1          1       2.0  4125.7 -52044
## - vertical1       1       2.1  4125.9 -52043
## - SD              1       2.7  4126.5 -52039
## - DAL             1       2.9  4126.7 -52037
## - NOR             1       3.0  4126.8 -52037
## - avg_rectd_plyr  1       4.3  4128.0 -52028
## - NE              1       5.0  4128.8 -52023
## - weight          1       5.7  4129.4 -52019
## - avg_rbry_plyr   1       7.0  4130.7 -52010
## - GB              1       7.7  4131.5 -52005
## - height          1      14.3  4138.1 -51961
## - avg_fuml_plyr   1      74.5  4198.2 -51565
## - avg_qbtdp_plyr  1    7702.8 11826.6 -23100
## 
## Step:  AIC=-52056.23
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - JAC             1       0.1  4123.9 -52058
## - DET             1       0.1  4123.9 -52058
## - grass_1         1       0.1  4123.9 -52057
## - hot_weather     1       0.1  4124.0 -52057
## - TEN             1       0.2  4124.0 -52057
## - home_team_1     1       0.2  4124.0 -52057
## - MINN            1       0.2  4124.1 -52057
## - NYJ             1       0.2  4124.1 -52057
## - KC              1       0.3  4124.1 -52056
## <none>                         4123.8 -52056
## - OAK             1       0.3  4124.2 -52056
## - DEN             1       0.4  4124.2 -52056
## - CHI             1       0.4  4124.2 -52055
## - ATL             1       0.4  4124.3 -52055
## - TB              1       0.6  4124.5 -52054
## - IND             1       0.8  4124.6 -52053
## - bad_weather_1   1       0.8  4124.6 -52053
## - CLE             1       0.8  4124.6 -52053
## - CIN             1       0.9  4124.7 -52052
## - WAS             1       1.1  4124.9 -52051
## - PHI             1       1.2  4125.1 -52050
## - HOU             1       1.3  4125.1 -52050
## - cold_weather    1       1.3  4125.1 -52049
## - avg_rbry_pos    1       1.5  4125.4 -52048
## - NYG             1       1.8  4125.7 -52046
## - forty1          1       2.0  4125.8 -52045
## - vertical1       1       2.1  4126.0 -52044
## - SD              1       2.6  4126.5 -52041
## - DAL             1       2.8  4126.7 -52039
## - NOR             1       3.0  4126.8 -52038
## - avg_rectd_plyr  1       4.3  4128.1 -52030
## - NE              1       4.9  4128.8 -52025
## - weight          1       5.7  4129.6 -52020
## - avg_rbry_plyr   1       7.0  4130.8 -52012
## - GB              1       7.7  4131.5 -52007
## - height          1      14.4  4138.2 -51963
## - avg_fuml_plyr   1      74.6  4198.5 -51565
## - avg_qbtdp_plyr  1    7704.2 11828.1 -23099
## 
## Step:  AIC=-52057.74
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - DET             1       0.1  4124.0 -52059
## - hot_weather     1       0.1  4124.0 -52059
## - grass_1         1       0.1  4124.0 -52059
## - TEN             1       0.1  4124.0 -52059
## - home_team_1     1       0.2  4124.1 -52059
## - NYJ             1       0.2  4124.1 -52058
## - MINN            1       0.3  4124.2 -52058
## - OAK             1       0.3  4124.2 -52058
## <none>                         4123.9 -52058
## - KC              1       0.3  4124.2 -52058
## - DEN             1       0.3  4124.2 -52058
## - CHI             1       0.4  4124.3 -52057
## - ATL             1       0.4  4124.3 -52057
## - TB              1       0.6  4124.5 -52056
## - IND             1       0.7  4124.6 -52055
## - bad_weather_1   1       0.8  4124.7 -52055
## - CIN             1       0.9  4124.8 -52054
## - CLE             1       0.9  4124.8 -52054
## - WAS             1       1.2  4125.1 -52052
## - cold_weather    1       1.3  4125.2 -52051
## - PHI             1       1.3  4125.2 -52051
## - HOU             1       1.3  4125.2 -52051
## - avg_rbry_pos    1       1.5  4125.4 -52050
## - NYG             1       1.8  4125.7 -52048
## - forty1          1       1.9  4125.9 -52047
## - vertical1       1       2.2  4126.1 -52045
## - SD              1       2.6  4126.5 -52043
## - DAL             1       2.8  4126.7 -52041
## - NOR             1       2.9  4126.8 -52040
## - avg_rectd_plyr  1       4.3  4128.2 -52031
## - NE              1       4.9  4128.8 -52027
## - weight          1       5.7  4129.6 -52022
## - avg_rbry_plyr   1       7.0  4130.9 -52013
## - GB              1       7.6  4131.5 -52009
## - height          1      14.4  4138.3 -51964
## - avg_fuml_plyr   1      74.7  4198.6 -51566
## - avg_qbtdp_plyr  1    7704.3 11828.2 -23100
## 
## Step:  AIC=-52059.21
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + 
##     GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + SD + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - TEN             1       0.1  4124.1 -52060
## - grass_1         1       0.1  4124.1 -52060
## - hot_weather     1       0.1  4124.1 -52060
## - home_team_1     1       0.2  4124.2 -52060
## - NYJ             1       0.2  4124.2 -52060
## - OAK             1       0.3  4124.3 -52059
## <none>                         4124.0 -52059
## - MINN            1       0.3  4124.3 -52059
## - DEN             1       0.3  4124.3 -52059
## - KC              1       0.3  4124.3 -52059
## - CHI             1       0.4  4124.3 -52059
## - ATL             1       0.4  4124.3 -52059
## - TB              1       0.5  4124.5 -52058
## - IND             1       0.7  4124.7 -52057
## - bad_weather_1   1       0.8  4124.8 -52056
## - CIN             1       0.8  4124.8 -52056
## - CLE             1       0.9  4124.9 -52055
## - WAS             1       1.2  4125.2 -52053
## - cold_weather    1       1.2  4125.2 -52053
## - PHI             1       1.4  4125.4 -52052
## - HOU             1       1.4  4125.4 -52052
## - avg_rbry_pos    1       1.5  4125.5 -52051
## - NYG             1       1.7  4125.7 -52050
## - forty1          1       1.9  4125.9 -52048
## - vertical1       1       2.2  4126.2 -52046
## - SD              1       2.5  4126.5 -52044
## - DAL             1       2.7  4126.7 -52043
## - NOR             1       2.8  4126.8 -52042
## - avg_rectd_plyr  1       4.4  4128.3 -52032
## - NE              1       4.8  4128.8 -52029
## - weight          1       5.7  4129.7 -52023
## - avg_rbry_plyr   1       6.9  4130.9 -52015
## - GB              1       7.5  4131.5 -52011
## - height          1      14.4  4138.4 -51965
## - avg_fuml_plyr   1      74.6  4198.6 -51568
## - avg_qbtdp_plyr  1    7704.4 11828.3 -23102
## 
## Step:  AIC=-52060.44
## py ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + 
##     GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - hot_weather     1       0.1  4124.2 -52062
## - grass_1         1       0.1  4124.2 -52061
## - home_team_1     1       0.2  4124.3 -52061
## - NYJ             1       0.2  4124.3 -52061
## - OAK             1       0.2  4124.3 -52061
## - DEN             1       0.3  4124.4 -52061
## <none>                         4124.1 -52060
## - CHI             1       0.3  4124.4 -52060
## - MINN            1       0.3  4124.4 -52060
## - ATL             1       0.3  4124.4 -52060
## - KC              1       0.4  4124.5 -52060
## - TB              1       0.5  4124.6 -52059
## - IND             1       0.6  4124.7 -52058
## - bad_weather_1   1       0.8  4124.9 -52057
## - CIN             1       0.8  4124.9 -52057
## - CLE             1       1.0  4125.1 -52056
## - cold_weather    1       1.2  4125.3 -52054
## - WAS             1       1.3  4125.4 -52054
## - PHI             1       1.5  4125.6 -52053
## - HOU             1       1.5  4125.6 -52053
## - avg_rbry_pos    1       1.5  4125.6 -52052
## - NYG             1       1.7  4125.8 -52051
## - forty1          1       1.9  4126.0 -52050
## - vertical1       1       2.3  4126.4 -52047
## - SD              1       2.4  4126.5 -52046
## - DAL             1       2.6  4126.7 -52045
## - NOR             1       2.8  4126.9 -52044
## - avg_rectd_plyr  1       4.3  4128.4 -52034
## - NE              1       4.7  4128.8 -52031
## - weight          1       5.7  4129.8 -52025
## - avg_rbry_plyr   1       6.9  4131.0 -52016
## - GB              1       7.4  4131.5 -52013
## - height          1      14.4  4138.5 -51967
## - avg_fuml_plyr   1      74.5  4198.6 -51570
## - avg_qbtdp_plyr  1    7714.1 11838.2 -23081
## 
## Step:  AIC=-52061.65
## py ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + GB + HOU + 
##     IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + SD + 
##     TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - grass_1         1       0.2  4124.4 -52063
## - home_team_1     1       0.2  4124.4 -52063
## - NYJ             1       0.2  4124.4 -52062
## - OAK             1       0.2  4124.5 -52062
## - DEN             1       0.3  4124.5 -52062
## <none>                         4124.2 -52062
## - CHI             1       0.3  4124.5 -52061
## - ATL             1       0.3  4124.6 -52061
## - MINN            1       0.3  4124.6 -52061
## - KC              1       0.4  4124.6 -52061
## - TB              1       0.5  4124.7 -52060
## - IND             1       0.6  4124.9 -52059
## - bad_weather_1   1       0.7  4125.0 -52059
## - CIN             1       0.8  4125.0 -52058
## - CLE             1       1.0  4125.2 -52057
## - cold_weather    1       1.2  4125.4 -52056
## - WAS             1       1.3  4125.5 -52055
## - PHI             1       1.5  4125.7 -52054
## - HOU             1       1.5  4125.7 -52054
## - avg_rbry_pos    1       1.5  4125.7 -52054
## - NYG             1       1.7  4125.9 -52052
## - forty1          1       1.9  4126.1 -52051
## - vertical1       1       2.3  4126.5 -52049
## - SD              1       2.5  4126.7 -52047
## - DAL             1       2.6  4126.9 -52046
## - NOR             1       2.8  4127.0 -52045
## - avg_rectd_plyr  1       4.3  4128.5 -52035
## - NE              1       4.7  4128.9 -52032
## - weight          1       5.7  4129.9 -52026
## - avg_rbry_plyr   1       6.9  4131.2 -52017
## - GB              1       7.4  4131.6 -52014
## - height          1      14.4  4138.6 -51968
## - avg_fuml_plyr   1      74.5  4198.7 -51571
## - avg_qbtdp_plyr  1    7714.5 11838.8 -23082
## 
## Step:  AIC=-52062.59
## py ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ATL + CHI + CIN + CLE + DAL + DEN + GB + HOU + 
##     IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + SD + 
##     TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - home_team_1     1       0.1  4124.5 -52064
## - NYJ             1       0.2  4124.5 -52064
## - OAK             1       0.3  4124.7 -52063
## <none>                         4124.4 -52063
## - ATL             1       0.3  4124.7 -52063
## - DEN             1       0.3  4124.7 -52062
## - KC              1       0.3  4124.7 -52062
## - CHI             1       0.4  4124.7 -52062
## - MINN            1       0.4  4124.8 -52062
## - TB              1       0.6  4124.9 -52061
## - IND             1       0.6  4125.0 -52061
## - CIN             1       0.7  4125.1 -52060
## - bad_weather_1   1       0.8  4125.1 -52059
## - CLE             1       0.9  4125.3 -52058
## - cold_weather    1       1.2  4125.6 -52056
## - WAS             1       1.3  4125.6 -52056
## - PHI             1       1.4  4125.8 -52055
## - avg_rbry_pos    1       1.5  4125.9 -52054
## - HOU             1       1.5  4125.9 -52054
## - NYG             1       1.6  4126.0 -52054
## - forty1          1       1.9  4126.3 -52052
## - vertical1       1       2.3  4126.6 -52050
## - DAL             1       2.6  4126.9 -52048
## - SD              1       2.7  4127.0 -52047
## - NOR             1       2.7  4127.1 -52047
## - avg_rectd_plyr  1       4.3  4128.7 -52036
## - NE              1       4.6  4129.0 -52034
## - weight          1       5.7  4130.1 -52027
## - avg_rbry_plyr   1       7.0  4131.3 -52018
## - GB              1       7.6  4131.9 -52014
## - height          1      14.4  4138.8 -51969
## - avg_fuml_plyr   1      74.5  4198.9 -51572
## - avg_qbtdp_plyr  1    7714.4 11838.8 -23084
## 
## Step:  AIC=-52063.82
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + SD + TB + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - NYJ             1       0.2  4124.6 -52065
## - OAK             1       0.3  4124.8 -52064
## - DEN             1       0.3  4124.8 -52064
## <none>                         4124.5 -52064
## - CHI             1       0.3  4124.8 -52064
## - KC              1       0.4  4124.8 -52063
## - ATL             1       0.4  4124.9 -52063
## - MINN            1       0.4  4124.9 -52063
## - TB              1       0.5  4125.0 -52062
## - IND             1       0.7  4125.1 -52061
## - CIN             1       0.7  4125.2 -52061
## - bad_weather_1   1       0.7  4125.2 -52061
## - CLE             1       1.0  4125.5 -52059
## - cold_weather    1       1.2  4125.7 -52058
## - WAS             1       1.3  4125.8 -52057
## - PHI             1       1.4  4125.9 -52056
## - HOU             1       1.5  4126.0 -52056
## - avg_rbry_pos    1       1.5  4126.0 -52056
## - NYG             1       1.6  4126.1 -52055
## - forty1          1       1.9  4126.4 -52053
## - vertical1       1       2.3  4126.7 -52051
## - SD              1       2.6  4127.1 -52048
## - DAL             1       2.7  4127.2 -52048
## - NOR             1       2.8  4127.3 -52047
## - avg_rectd_plyr  1       4.3  4128.8 -52037
## - NE              1       4.5  4129.0 -52036
## - weight          1       5.7  4130.2 -52028
## - avg_rbry_plyr   1       6.9  4131.4 -52020
## - GB              1       7.5  4132.0 -52016
## - height          1      14.4  4138.9 -51970
## - avg_fuml_plyr   1      74.5  4199.0 -51574
## - avg_qbtdp_plyr  1    7715.0 11839.5 -23084
## 
## Step:  AIC=-52064.8
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + 
##     NE + NOR + NYG + OAK + PHI + SD + TB + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - OAK             1       0.2  4124.9 -52065
## - DEN             1       0.3  4124.9 -52065
## <none>                         4124.6 -52065
## - CHI             1       0.3  4125.0 -52065
## - ATL             1       0.3  4125.0 -52065
## - KC              1       0.4  4125.0 -52064
## - MINN            1       0.4  4125.1 -52064
## - TB              1       0.5  4125.1 -52063
## - IND             1       0.6  4125.3 -52063
## - CIN             1       0.7  4125.3 -52062
## - bad_weather_1   1       0.7  4125.4 -52062
## - CLE             1       1.0  4125.7 -52060
## - cold_weather    1       1.2  4125.9 -52059
## - WAS             1       1.4  4126.0 -52058
## - NYG             1       1.5  4126.2 -52057
## - PHI             1       1.5  4126.2 -52057
## - avg_rbry_pos    1       1.5  4126.2 -52057
## - HOU             1       1.5  4126.2 -52056
## - forty1          1       1.9  4126.5 -52054
## - vertical1       1       2.3  4127.0 -52051
## - SD              1       2.5  4127.2 -52050
## - DAL             1       2.7  4127.3 -52049
## - NOR             1       2.7  4127.3 -52049
## - avg_rectd_plyr  1       4.3  4128.9 -52038
## - NE              1       4.4  4129.1 -52037
## - weight          1       5.7  4130.3 -52029
## - avg_rbry_plyr   1       7.0  4131.6 -52020
## - GB              1       7.4  4132.0 -52018
## - height          1      14.4  4139.0 -51971
## - avg_fuml_plyr   1      74.4  4199.0 -51576
## - avg_qbtdp_plyr  1    7722.0 11846.6 -23070
## 
## Step:  AIC=-52065.2
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + 
##     NE + NOR + NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - DEN             1       0.2  4125.1 -52066
## - CHI             1       0.3  4125.2 -52065
## - ATL             1       0.3  4125.2 -52065
## <none>                         4124.9 -52065
## - KC              1       0.4  4125.3 -52064
## - TB              1       0.5  4125.3 -52064
## - MINN            1       0.5  4125.4 -52064
## - IND             1       0.6  4125.4 -52063
## - CIN             1       0.6  4125.5 -52063
## - bad_weather_1   1       0.8  4125.6 -52062
## - CLE             1       1.1  4126.0 -52060
## - cold_weather    1       1.2  4126.1 -52059
## - NYG             1       1.4  4126.3 -52058
## - WAS             1       1.5  4126.3 -52058
## - avg_rbry_pos    1       1.5  4126.4 -52057
## - PHI             1       1.6  4126.5 -52057
## - HOU             1       1.7  4126.5 -52056
## - forty1          1       2.0  4126.8 -52054
## - vertical1       1       2.3  4127.2 -52052
## - SD              1       2.4  4127.3 -52051
## - DAL             1       2.6  4127.4 -52050
## - NOR             1       2.6  4127.5 -52050
## - avg_rectd_plyr  1       4.2  4129.1 -52039
## - NE              1       4.3  4129.2 -52038
## - weight          1       5.6  4130.5 -52030
## - avg_rbry_plyr   1       6.9  4131.8 -52021
## - GB              1       7.2  4132.1 -52019
## - height          1      14.2  4139.1 -51973
## - avg_fuml_plyr   1      74.6  4199.5 -51574
## - avg_qbtdp_plyr  1    7721.7 11846.6 -23072
## 
## Step:  AIC=-52065.64
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + GB + HOU + IND + KC + MINN + NE + 
##     NOR + NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - CHI             1       0.2  4125.4 -52066
## - ATL             1       0.3  4125.4 -52066
## <none>                         4125.1 -52066
## - TB              1       0.4  4125.5 -52065
## - KC              1       0.5  4125.6 -52064
## - IND             1       0.5  4125.6 -52064
## - MINN            1       0.5  4125.6 -52064
## - CIN             1       0.6  4125.7 -52064
## - bad_weather_1   1       0.7  4125.9 -52063
## - CLE             1       1.2  4126.3 -52060
## - cold_weather    1       1.2  4126.3 -52060
## - NYG             1       1.4  4126.5 -52059
## - avg_rbry_pos    1       1.5  4126.6 -52058
## - WAS             1       1.5  4126.7 -52057
## - PHI             1       1.7  4126.8 -52056
## - HOU             1       1.7  4126.9 -52056
## - forty1          1       1.9  4127.0 -52055
## - vertical1       1       2.3  4127.5 -52052
## - SD              1       2.4  4127.5 -52052
## - DAL             1       2.5  4127.6 -52051
## - NOR             1       2.5  4127.6 -52051
## - NE              1       4.2  4129.3 -52040
## - avg_rectd_plyr  1       4.3  4129.5 -52039
## - weight          1       5.6  4130.7 -52031
## - avg_rbry_plyr   1       6.9  4132.0 -52022
## - GB              1       7.1  4132.2 -52020
## - height          1      14.3  4139.4 -51973
## - avg_fuml_plyr   1      74.6  4199.7 -51575
## - avg_qbtdp_plyr  1    7722.8 11847.9 -23070
## 
## Step:  AIC=-52066
## py ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CIN + CLE + DAL + GB + HOU + IND + KC + MINN + NE + NOR + 
##     NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - ATL             1       0.2  4125.6 -52066
## <none>                         4125.4 -52066
## - TB              1       0.4  4125.7 -52065
## - IND             1       0.5  4125.8 -52065
## - CIN             1       0.5  4125.9 -52065
## - KC              1       0.5  4125.9 -52064
## - MINN            1       0.6  4125.9 -52064
## - bad_weather_1   1       0.8  4126.1 -52063
## - cold_weather    1       1.3  4126.6 -52060
## - CLE             1       1.3  4126.6 -52060
## - NYG             1       1.3  4126.7 -52059
## - avg_rbry_pos    1       1.5  4126.8 -52058
## - WAS             1       1.6  4127.0 -52057
## - PHI             1       1.8  4127.2 -52056
## - HOU             1       1.8  4127.2 -52056
## - forty1          1       1.9  4127.3 -52055
## - SD              1       2.3  4127.6 -52053
## - vertical1       1       2.3  4127.6 -52053
## - DAL             1       2.4  4127.8 -52052
## - NOR             1       2.4  4127.8 -52052
## - NE              1       4.1  4129.5 -52041
## - avg_rectd_plyr  1       4.3  4129.7 -52039
## - weight          1       5.5  4130.9 -52031
## - GB              1       6.9  4132.3 -52022
## - avg_rbry_plyr   1       6.9  4132.3 -52022
## - height          1      14.1  4139.5 -51974
## - avg_fuml_plyr   1      74.4  4199.8 -51577
## - avg_qbtdp_plyr  1    7733.1 11858.5 -23048
## 
## Step:  AIC=-52066.44
## py ~ height + weight + cold_weather + forty1 + vertical1 + CIN + 
##     CLE + DAL + GB + HOU + IND + KC + MINN + NE + NOR + NYG + 
##     PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## <none>                         4125.6 -52066
## - TB              1       0.3  4125.9 -52066
## - IND             1       0.4  4126.0 -52066
## - CIN             1       0.5  4126.1 -52065
## - KC              1       0.6  4126.2 -52065
## - MINN            1       0.6  4126.2 -52064
## - bad_weather_1   1       0.8  4126.4 -52063
## - cold_weather    1       1.2  4126.8 -52061
## - NYG             1       1.2  4126.8 -52060
## - CLE             1       1.3  4126.9 -52060
## - avg_rbry_pos    1       1.5  4127.1 -52059
## - WAS             1       1.7  4127.3 -52057
## - PHI             1       1.9  4127.5 -52056
## - forty1          1       1.9  4127.5 -52056
## - HOU             1       1.9  4127.5 -52056
## - SD              1       2.2  4127.8 -52054
## - vertical1       1       2.2  4127.8 -52054
## - DAL             1       2.3  4127.9 -52053
## - NOR             1       2.3  4127.9 -52053
## - NE              1       4.0  4129.6 -52042
## - avg_rectd_plyr  1       4.5  4130.1 -52039
## - weight          1       5.5  4131.1 -52032
## - GB              1       6.8  4132.4 -52023
## - avg_rbry_plyr   1       7.0  4132.6 -52022
## - height          1      14.3  4139.9 -51973
## - avg_fuml_plyr   1      75.1  4200.7 -51573
## - avg_qbtdp_plyr  1    7746.2 11871.8 -23019

Conclusion, this predicts well, but it seems like this could be driven by some chance. QB statistics remind me of baseball statistics. One batter vs One pitcher. A QB is really like a pitcher or a batter. The opponent is more complex, however one side of the equation is “controlled”.

Pass completions

PreProcess:

set.seed(123)
splitpc <- sample.split(nfl_data$pc, SplitRatio = 0.7)
Trainpc <- subset(nfl_data, split == TRUE)
Testpc <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainpc, method = c("center", "scale"))
trainTransformedpc <- predict(preProcValues, Trainpc)
testTransformedpc <- predict(preProcValues, Testpc)

ggpairs:

ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("pc",colnames(filtered_nfl_data_fields[46:51]))])

pcregform <- formula(paste("pc ~ ", 
                           paste(colnames(filtered_nfl_data_fields), collapse="+")))


linRegQBpc <- lm(pcregform, data = trainTransformedpc)
summary(linRegQBpc)
## 
## Call:
## lm(formula = pcregform, data = trainTransformedpc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2064 -0.0581 -0.0134  0.0334  4.6794 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      6.619e-16  2.292e-03   0.000  1.00000    
## height           4.875e-02  4.447e-03  10.962  < 2e-16 ***
## weight          -3.307e-02  4.168e-03  -7.934 2.20e-15 ***
## cold_weather    -6.023e-03  2.413e-03  -2.497  0.01255 *  
## hot_weather     -1.998e-03  2.313e-03  -0.864  0.38767    
## home_team_1     -4.305e-04  2.494e-03  -0.173  0.86295    
## forty1           1.912e-02  3.956e-03   4.834 1.34e-06 ***
## vertical1       -1.573e-02  3.041e-03  -5.171 2.35e-07 ***
## ARI             -5.917e-04  3.206e-03  -0.185  0.85358    
## ATL             -4.000e-03  3.222e-03  -1.242  0.21435    
## BAL              7.475e-05  3.224e-03   0.023  0.98150    
## BUF              1.988e-03  3.183e-03   0.624  0.53234    
## CAR             -3.205e-03  3.162e-03  -1.013  0.31086    
## CHI             -4.804e-03  3.127e-03  -1.536  0.12448    
## CIN             -3.230e-03  3.184e-03  -1.014  0.31044    
## CLE              7.483e-03  3.170e-03   2.361  0.01824 *  
## DAL             -1.007e-02  3.202e-03  -3.144  0.00167 ** 
## DEN             -5.680e-03  3.214e-03  -1.767  0.07723 .  
## DET             -2.677e-03  3.170e-03  -0.844  0.39848    
## GB              -1.886e-02  3.263e-03  -5.779 7.61e-09 ***
## HOU              7.485e-03  3.224e-03   2.321  0.02028 *  
## IND             -5.768e-03  3.201e-03  -1.802  0.07155 .  
## JAC              1.020e-03  3.122e-03   0.327  0.74386    
## KC               6.030e-03  3.191e-03   1.890  0.05880 .  
## MIA              5.780e-04  3.139e-03   0.184  0.85392    
## MINN             6.798e-03  3.159e-03   2.152  0.03140 *  
## NE              -1.660e-02  3.299e-03  -5.031 4.91e-07 ***
## NOR             -8.839e-03  3.289e-03  -2.688  0.00720 ** 
## NYG             -9.940e-03  3.214e-03  -3.092  0.00199 ** 
## NYJ             -3.931e-03  3.203e-03  -1.227  0.21971    
## OAK             -3.317e-03  3.223e-03  -1.029  0.30332    
## PHI              5.894e-03  3.123e-03   1.887  0.05911 .  
## PIT             -2.766e-03  3.205e-03  -0.863  0.38812    
## SD              -1.241e-02  3.145e-03  -3.945 7.98e-05 ***
## SEA             -6.289e-05  3.264e-03  -0.019  0.98463    
## STL              2.845e-03  3.177e-03   0.896  0.37046    
## TB              -6.705e-03  3.147e-03  -2.130  0.03314 *  
## TEN             -4.097e-03  3.166e-03  -1.294  0.19569    
## WAS              5.572e-03  3.183e-03   1.751  0.08002 .  
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -1.563e-02  2.927e-03  -5.340 9.35e-08 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr   -3.018e-02  3.503e-03  -8.616  < 2e-16 ***
## avg_rbry_pos     1.899e-02  4.081e-03   4.654 3.27e-06 ***
## avg_fuml_plyr    7.949e-02  3.386e-03  23.477  < 2e-16 ***
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr   8.437e-01  3.678e-03 229.388  < 2e-16 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -1.757e-03  2.637e-03  -0.666  0.50524    
## bad_weather_1   -5.132e-03  2.332e-03  -2.201  0.02775 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.38 on 27438 degrees of freedom
## Multiple R-squared:  0.8558, Adjusted R-squared:  0.8556 
## F-statistic:  3620 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegQBpc2 <- update(linRegQBpc, ~.-hot_weather-home_team_1-vertical1-ATL-BAL-CIN-DAL-DEN-DET-KC
                      -MIA-PHI-PIT-SEA-STL-WAS-avg_trg_team-avg_tdr_team-avg_rbra_team
                      -avg_rbry_plyr-avg_fuml_team-avg_qbints_team-avg_qbtdp_team-grass_1 )
summary(linRegQBpc2)
## 
## Call:
## lm(formula = pc ~ height + weight + cold_weather + forty1 + ARI + 
##     BUF + CAR + CHI + CLE + GB + HOU + IND + JAC + MINN + NE + 
##     NOR + NYG + NYJ + OAK + SD + TB + TEN + avg_rectd_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1, 
##     data = trainTransformedpc)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2398 -0.0575 -0.0124  0.0294  4.6660 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     7.666e-16  2.298e-03   0.000 1.000000    
## height          4.709e-02  4.435e-03  10.619  < 2e-16 ***
## weight         -3.546e-02  4.143e-03  -8.558  < 2e-16 ***
## cold_weather   -5.546e-03  2.366e-03  -2.344 0.019063 *  
## forty1          3.370e-02  3.324e-03  10.139  < 2e-16 ***
## ARI             1.021e-03  2.347e-03   0.435 0.663685    
## BUF             3.111e-03  2.346e-03   1.326 0.184868    
## CAR            -3.434e-03  2.345e-03  -1.464 0.143092    
## CHI            -4.221e-03  2.347e-03  -1.798 0.072184 .  
## CLE             7.582e-03  2.354e-03   3.221 0.001279 ** 
## GB             -1.833e-02  2.367e-03  -7.744 9.98e-15 ***
## HOU             7.470e-03  2.354e-03   3.173 0.001512 ** 
## IND            -5.380e-03  2.344e-03  -2.295 0.021764 *  
## JAC             6.082e-04  2.343e-03   0.260 0.795205    
## MINN            6.319e-03  2.350e-03   2.689 0.007163 ** 
## NE             -1.631e-02  2.395e-03  -6.809 1.00e-11 ***
## NOR            -7.575e-03  2.363e-03  -3.205 0.001350 ** 
## NYG            -8.832e-03  2.348e-03  -3.761 0.000169 ***
## NYJ            -4.421e-03  2.345e-03  -1.885 0.059386 .  
## OAK            -1.986e-03  2.360e-03  -0.841 0.400133    
## SD             -1.167e-02  2.347e-03  -4.973 6.63e-07 ***
## TB             -6.022e-03  2.346e-03  -2.568 0.010247 *  
## TEN            -3.866e-03  2.346e-03  -1.648 0.099462 .  
## avg_rectd_plyr -1.860e-02  2.908e-03  -6.396 1.62e-10 ***
## avg_rbry_pos   -5.369e-04  3.417e-03  -0.157 0.875164    
## avg_fuml_plyr   7.127e-02  3.185e-03  22.374  < 2e-16 ***
## avg_qbtdp_plyr  8.468e-01  3.635e-03 232.924  < 2e-16 ***
## bad_weather_1  -5.320e-03  2.332e-03  -2.281 0.022535 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3809 on 27456 degrees of freedom
## Multiple R-squared:  0.855,  Adjusted R-squared:  0.8549 
## F-statistic:  5998 on 27 and 27456 DF,  p-value: < 2.2e-16

Again, R2 is very strong, model stays strong when model is shrunk to 8 variables. Not surprising (to me) bad weather and cold weather hurt completions. It is harder to throw a ball in bad weather and catch a ball in bad weather.

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

PcPredicted <- predict(linRegQBpc2, newdata = testTransformedpc)

SSEpc <- sum((PcPredicted - testTransformedpc$pc)^2)
SSTpc <- sum((mean(nfl_data$pc)-testTransformedpc$pc)^2)
r2_pc <- 1 - SSEpc/SSTpc 
r2_pc
## [1] 0.9703489
rmse_pc <- sqrt(SSEpc/nrow(testTransformedpc))
rmse_pc
## [1] 0.3924396

Regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBpc2, which = c(1:3,5))

Very similar problems/characteristics as we saw in yards

Summary statistics:

confint(linRegQBpc2)
##                       2.5 %        97.5 %
## (Intercept)    -0.004503758  0.0045037581
## height          0.038398997  0.0557838535
## weight         -0.043577952 -0.0273367386
## cold_weather   -0.010182362 -0.0009092848
## forty1          0.027185053  0.0402147931
## ARI            -0.003579930  0.0056211955
## BUF            -0.001487868  0.0077103207
## CAR            -0.008031261  0.0011623957
## CHI            -0.008821661  0.0003803371
## CLE             0.002968402  0.0121965425
## GB             -0.022967535 -0.0136892607
## HOU             0.002855127  0.0120843132
## IND            -0.009974835 -0.0007843123
## JAC            -0.003984834  0.0052013096
## MINN            0.001713726  0.0109249709
## NE             -0.020998638 -0.0116116817
## NOR            -0.012207381 -0.0029431848
## NYG            -0.013434167 -0.0042295072
## NYJ            -0.009016369  0.0001750304
## OAK            -0.006612556  0.0026404775
## SD             -0.016274935 -0.0070726373
## TB             -0.010619902 -0.0014249439
## TEN            -0.008464463  0.0007332893
## avg_rectd_plyr -0.024300118 -0.0129002712
## avg_rbry_pos   -0.007235219  0.0061614368
## avg_fuml_plyr   0.065021908  0.0775083344
## avg_qbtdp_plyr  0.839643262  0.8538943403
## bad_weather_1  -0.009890038 -0.0007491984
coef(summary(linRegQBpc2))
##                     Estimate  Std. Error       t value      Pr(>|t|)
## (Intercept)     7.666331e-16 0.002297777  3.336412e-13  1.000000e+00
## height          4.709143e-02 0.004434798  1.061862e+01  2.745893e-26
## weight         -3.545735e-02 0.004143060 -8.558250e+00  1.204789e-17
## cold_weather   -5.545823e-03 0.002365520 -2.344441e+00  1.906269e-02
## forty1          3.369992e-02 0.003323828  1.013889e+01  4.094619e-24
## ARI             1.020633e-03 0.002347165  4.348364e-01  6.636846e-01
## BUF             3.111226e-03 0.002346417  1.325948e+00  1.848680e-01
## CAR            -3.434433e-03 0.002345260 -1.464414e+00  1.430922e-01
## CHI            -4.220662e-03 0.002347388 -1.798025e+00  7.218407e-02
## CLE             7.582472e-03 0.002354057  3.221023e+00  1.278825e-03
## GB             -1.832840e-02 0.002366846 -7.743807e+00  9.979816e-15
## HOU             7.469720e-03 0.002354324  3.172767e+00  1.511602e-03
## IND            -5.379574e-03 0.002344461 -2.294589e+00  2.176421e-02
## JAC             6.082379e-04 0.002343344  2.595598e-01  7.952053e-01
## MINN            6.319349e-03 0.002349747  2.689374e+00  7.162938e-03
## NE             -1.630516e-02 0.002394570 -6.809222e+00  1.001490e-11
## NOR            -7.575283e-03 0.002363254 -3.205445e+00  1.350080e-03
## NYG            -8.831837e-03 0.002348067 -3.761322e+00  1.693684e-04
## NYJ            -4.420669e-03 0.002344684 -1.885400e+00  5.938634e-02
## OAK            -1.986039e-03 0.002360407 -8.413970e-01  4.001329e-01
## SD             -1.167379e-02 0.002347465 -4.972934e+00  6.634458e-07
## TB             -6.022423e-03 0.002345592 -2.567549e+00  1.024728e-02
## TEN            -3.865587e-03 0.002346305 -1.647521e+00  9.946244e-02
## avg_rectd_plyr -1.860019e-02 0.002908049 -6.396107e+00  1.619528e-10
## avg_rbry_pos   -5.368910e-04 0.003417426 -1.571039e-01  8.751641e-01
## avg_fuml_plyr   7.126512e-02 0.003185231  2.237361e+01 6.839892e-110
## avg_qbtdp_plyr  8.467688e-01 0.003635386  2.329241e+02  0.000000e+00
## bad_weather_1  -5.319618e-03 0.002331787 -2.281348e+00  2.253546e-02
anova(linRegQBpc2)
## Analysis of Variance Table
## 
## Response: pc
##                   Df Sum Sq Mean Sq    F value    Pr(>F)    
## height             1 1882.8  1882.8 12974.7620 < 2.2e-16 ***
## weight             1  461.2   461.2  3178.5347 < 2.2e-16 ***
## cold_weather       1    0.5     0.5     3.7567  0.052607 .  
## forty1             1 5589.0  5589.0 38515.7304 < 2.2e-16 ***
## ARI                1    0.3     0.3     2.1068  0.146660    
## BUF                1    0.9     0.9     6.3007  0.012075 *  
## CAR                1    6.9     6.9    47.7623 4.917e-12 ***
## CHI                1    0.2     0.2     1.2414  0.265216    
## CLE                1    1.1     1.1     7.2861  0.006953 ** 
## GB                 1    0.0     0.0     0.0309  0.860535    
## HOU                1   13.9    13.9    95.9656 < 2.2e-16 ***
## IND                1   11.5    11.5    79.0848 < 2.2e-16 ***
## JAC                1    0.1     0.1     0.9519  0.329253    
## MINN               1    0.4     0.4     2.9212  0.087437 .  
## NE                 1   36.9    36.9   254.3033 < 2.2e-16 ***
## NOR                1   16.0    16.0   110.5203 < 2.2e-16 ***
## NYG                1    6.4     6.4    43.9986 3.347e-11 ***
## NYJ                1    0.4     0.4     3.0309  0.081702 .  
## OAK                1    0.8     0.8     5.7241  0.016740 *  
## SD                 1   12.4    12.4    85.4687 < 2.2e-16 ***
## TB                 1    2.3     2.3    15.6288 7.727e-05 ***
## TEN                1    4.4     4.4    30.1061 4.127e-08 ***
## avg_rectd_plyr     1 1862.7  1862.7 12836.4447 < 2.2e-16 ***
## avg_rbry_pos       1  322.4   322.4  2221.7472 < 2.2e-16 ***
## avg_fuml_plyr      1 5391.9  5391.9 37157.5723 < 2.2e-16 ***
## avg_qbtdp_plyr     1 7872.6  7872.6 54252.8371 < 2.2e-16 ***
## bad_weather_1      1    0.8     0.8     5.2046  0.022535 *  
## Residuals      27456 3984.1     0.1                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_pc <- step(lm(pcregform, data = trainTransformedpc), direction = "backward")
## Start:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-53141.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - SEA             1       0.0  3961.8 -53144
## - BAL             1       0.0  3961.8 -53144
## - home_team_1     1       0.0  3961.8 -53144
## - MIA             1       0.0  3961.8 -53144
## - ARI             1       0.0  3961.8 -53144
## - JAC             1       0.0  3961.9 -53144
## - BUF             1       0.1  3961.9 -53143
## - grass_1         1       0.1  3961.9 -53143
## - DET             1       0.1  3961.9 -53143
## - PIT             1       0.1  3961.9 -53143
## - hot_weather     1       0.1  3961.9 -53143
## - STL             1       0.1  3962.0 -53143
## - CAR             1       0.1  3962.0 -53143
## - CIN             1       0.1  3962.0 -53143
## - OAK             1       0.2  3962.0 -53143
## - NYJ             1       0.2  3962.1 -53142
## - ATL             1       0.2  3962.1 -53142
## - TEN             1       0.2  3962.1 -53142
## <none>                         3961.8 -53142
## - CHI             1       0.3  3962.2 -53141
## - WAS             1       0.4  3962.3 -53141
## - DEN             1       0.5  3962.3 -53141
## - IND             1       0.5  3962.3 -53140
## - PHI             1       0.5  3962.4 -53140
## - KC              1       0.5  3962.4 -53140
## - TB              1       0.7  3962.5 -53139
## - MINN            1       0.7  3962.5 -53139
## - bad_weather_1   1       0.7  3962.5 -53139
## - HOU             1       0.8  3962.6 -53138
## - CLE             1       0.8  3962.6 -53138
## - cold_weather    1       0.9  3962.7 -53137
## - NOR             1       1.0  3962.9 -53136
## - NYG             1       1.4  3963.2 -53134
## - DAL             1       1.4  3963.3 -53134
## - SD              1       2.2  3964.1 -53128
## - avg_rbry_pos    1       3.1  3965.0 -53122
## - forty1          1       3.4  3965.2 -53120
## - NE              1       3.7  3965.5 -53118
## - vertical1       1       3.9  3965.7 -53117
## - avg_rectd_plyr  1       4.1  3966.0 -53115
## - GB              1       4.8  3966.7 -53110
## - weight          1       9.1  3970.9 -53081
## - avg_rbry_plyr   1      10.7  3972.6 -53069
## - height          1      17.4  3979.2 -53024
## - avg_fuml_plyr   1      79.6  4041.4 -52597
## - avg_qbtdp_plyr  1    7597.8 11559.6 -23714
## 
## Step:  AIC=-53143.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BAL             1       0.0  3961.8 -53146
## - home_team_1     1       0.0  3961.8 -53146
## - ARI             1       0.0  3961.8 -53146
## - MIA             1       0.0  3961.8 -53146
## - JAC             1       0.0  3961.9 -53145
## - grass_1         1       0.1  3961.9 -53145
## - BUF             1       0.1  3961.9 -53145
## - hot_weather     1       0.1  3961.9 -53145
## - DET             1       0.1  3962.0 -53145
## - PIT             1       0.1  3962.0 -53145
## - STL             1       0.2  3962.0 -53145
## - CAR             1       0.2  3962.0 -53144
## - CIN             1       0.2  3962.0 -53144
## - OAK             1       0.2  3962.0 -53144
## <none>                         3961.8 -53144
## - NYJ             1       0.3  3962.1 -53144
## - ATL             1       0.3  3962.1 -53144
## - TEN             1       0.3  3962.2 -53143
## - CHI             1       0.4  3962.3 -53143
## - WAS             1       0.6  3962.4 -53142
## - DEN             1       0.6  3962.4 -53142
## - IND             1       0.6  3962.5 -53141
## - PHI             1       0.7  3962.5 -53141
## - KC              1       0.7  3962.5 -53141
## - bad_weather_1   1       0.7  3962.5 -53141
## - TB              1       0.9  3962.7 -53140
## - MINN            1       0.9  3962.7 -53139
## - cold_weather    1       0.9  3962.7 -53139
## - HOU             1       1.0  3962.9 -53138
## - CLE             1       1.1  3962.9 -53138
## - NOR             1       1.4  3963.3 -53136
## - NYG             1       1.9  3963.7 -53133
## - DAL             1       1.9  3963.7 -53133
## - SD              1       2.9  3964.8 -53125
## - avg_rbry_pos    1       3.1  3965.0 -53124
## - forty1          1       3.4  3965.2 -53122
## - vertical1       1       3.9  3965.7 -53119
## - avg_rectd_plyr  1       4.1  3966.0 -53117
## - NE              1       5.0  3966.8 -53111
## - GB              1       6.5  3968.3 -53101
## - weight          1       9.1  3970.9 -53083
## - avg_rbry_plyr   1      10.7  3972.6 -53071
## - height          1      17.4  3979.2 -53026
## - avg_fuml_plyr   1      79.6  4041.5 -52599
## - avg_qbtdp_plyr  1    7604.3 11566.1 -23700
## 
## Step:  AIC=-53145.63
## pc ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - home_team_1     1       0.0  3961.8 -53148
## - MIA             1       0.0  3961.8 -53148
## - ARI             1       0.0  3961.8 -53148
## - JAC             1       0.0  3961.9 -53147
## - grass_1         1       0.1  3961.9 -53147
## - BUF             1       0.1  3961.9 -53147
## - hot_weather     1       0.1  3961.9 -53147
## - DET             1       0.2  3962.0 -53147
## - PIT             1       0.2  3962.0 -53147
## - STL             1       0.2  3962.0 -53146
## - CAR             1       0.2  3962.1 -53146
## - CIN             1       0.2  3962.1 -53146
## - OAK             1       0.2  3962.1 -53146
## <none>                         3961.8 -53146
## - NYJ             1       0.3  3962.2 -53145
## - ATL             1       0.3  3962.2 -53145
## - TEN             1       0.4  3962.2 -53145
## - CHI             1       0.5  3962.3 -53144
## - WAS             1       0.7  3962.5 -53143
## - DEN             1       0.7  3962.5 -53143
## - bad_weather_1   1       0.7  3962.5 -53143
## - IND             1       0.7  3962.5 -53143
## - PHI             1       0.7  3962.6 -53142
## - KC              1       0.8  3962.6 -53142
## - cold_weather    1       0.9  3962.7 -53141
## - TB              1       1.0  3962.8 -53141
## - MINN            1       1.0  3962.8 -53141
## - HOU             1       1.2  3963.0 -53140
## - CLE             1       1.2  3963.0 -53139
## - NOR             1       1.6  3963.4 -53136
## - NYG             1       2.1  3963.9 -53133
## - DAL             1       2.1  3964.0 -53133
## - avg_rbry_pos    1       3.1  3965.0 -53126
## - SD              1       3.3  3965.1 -53125
## - forty1          1       3.4  3965.2 -53124
## - vertical1       1       3.9  3965.7 -53121
## - avg_rectd_plyr  1       4.1  3966.0 -53119
## - NE              1       5.6  3967.4 -53109
## - GB              1       7.3  3969.2 -53097
## - weight          1       9.1  3970.9 -53085
## - avg_rbry_plyr   1      10.7  3972.6 -53073
## - height          1      17.4  3979.2 -53027
## - avg_fuml_plyr   1      79.6  4041.5 -52601
## - avg_qbtdp_plyr  1    7605.8 11567.7 -23698
## 
## Step:  AIC=-53147.6
## pc ~ height + weight + cold_weather + hot_weather + forty1 + 
##     vertical1 + ARI + ATL + BUF + CAR + CHI + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - ARI             1       0.0  3961.9 -53150
## - MIA             1       0.0  3961.9 -53150
## - JAC             1       0.0  3961.9 -53149
## - grass_1         1       0.1  3961.9 -53149
## - BUF             1       0.1  3961.9 -53149
## - hot_weather     1       0.1  3962.0 -53149
## - DET             1       0.1  3962.0 -53149
## - PIT             1       0.2  3962.0 -53148
## - STL             1       0.2  3962.0 -53148
## - CAR             1       0.2  3962.1 -53148
## - CIN             1       0.2  3962.1 -53148
## - OAK             1       0.2  3962.1 -53148
## <none>                         3961.8 -53148
## - ATL             1       0.3  3962.2 -53147
## - NYJ             1       0.3  3962.2 -53147
## - TEN             1       0.4  3962.2 -53147
## - CHI             1       0.5  3962.3 -53146
## - WAS             1       0.7  3962.5 -53145
## - DEN             1       0.7  3962.5 -53145
## - IND             1       0.7  3962.5 -53145
## - bad_weather_1   1       0.7  3962.5 -53145
## - PHI             1       0.7  3962.6 -53144
## - KC              1       0.8  3962.6 -53144
## - cold_weather    1       0.9  3962.8 -53143
## - TB              1       1.0  3962.8 -53143
## - MINN            1       1.0  3962.8 -53143
## - CLE             1       1.2  3963.0 -53141
## - HOU             1       1.2  3963.0 -53141
## - NOR             1       1.6  3963.4 -53138
## - NYG             1       2.1  3963.9 -53135
## - DAL             1       2.1  3964.0 -53135
## - avg_rbry_pos    1       3.1  3965.0 -53128
## - SD              1       3.3  3965.1 -53127
## - forty1          1       3.4  3965.2 -53126
## - vertical1       1       3.9  3965.7 -53123
## - avg_rectd_plyr  1       4.1  3966.0 -53121
## - NE              1       5.6  3967.5 -53111
## - GB              1       7.3  3969.2 -53099
## - weight          1       9.1  3970.9 -53087
## - avg_rbry_plyr   1      10.7  3972.6 -53075
## - height          1      17.4  3979.2 -53029
## - avg_fuml_plyr   1      79.6  4041.5 -52603
## - avg_qbtdp_plyr  1    7606.0 11567.8 -23700
## 
## Step:  AIC=-53149.56
## pc ~ height + weight + cold_weather + hot_weather + forty1 + 
##     vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + 
##     NYG + NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - MIA             1       0.0  3961.9 -53151
## - JAC             1       0.0  3961.9 -53151
## - grass_1         1       0.1  3961.9 -53151
## - BUF             1       0.1  3962.0 -53151
## - hot_weather     1       0.1  3962.0 -53151
## - DET             1       0.1  3962.0 -53151
## - PIT             1       0.2  3962.0 -53150
## - STL             1       0.2  3962.1 -53150
## - CAR             1       0.2  3962.1 -53150
## - CIN             1       0.2  3962.1 -53150
## - OAK             1       0.2  3962.1 -53150
## <none>                         3961.9 -53150
## - ATL             1       0.3  3962.2 -53149
## - NYJ             1       0.3  3962.2 -53149
## - TEN             1       0.4  3962.2 -53149
## - CHI             1       0.5  3962.3 -53148
## - DEN             1       0.7  3962.5 -53147
## - bad_weather_1   1       0.7  3962.6 -53147
## - IND             1       0.7  3962.6 -53147
## - WAS             1       0.7  3962.6 -53147
## - PHI             1       0.8  3962.7 -53146
## - KC              1       0.8  3962.7 -53146
## - cold_weather    1       0.9  3962.8 -53145
## - TB              1       1.0  3962.8 -53145
## - MINN            1       1.1  3962.9 -53144
## - CLE             1       1.3  3963.1 -53143
## - HOU             1       1.3  3963.2 -53142
## - NOR             1       1.7  3963.5 -53140
## - NYG             1       2.2  3964.0 -53136
## - DAL             1       2.2  3964.1 -53136
## - avg_rbry_pos    1       3.1  3965.0 -53130
## - SD              1       3.4  3965.2 -53128
## - forty1          1       3.4  3965.2 -53128
## - vertical1       1       3.9  3965.7 -53125
## - avg_rectd_plyr  1       4.1  3966.0 -53123
## - NE              1       5.8  3967.7 -53111
## - GB              1       7.7  3969.5 -53098
## - weight          1       9.1  3970.9 -53089
## - avg_rbry_plyr   1      10.7  3972.6 -53077
## - height          1      17.4  3979.2 -53031
## - avg_fuml_plyr   1      79.7  4041.5 -52604
## - avg_qbtdp_plyr  1    7617.6 11579.4 -23674
## 
## Step:  AIC=-53151.48
## pc ~ height + weight + cold_weather + hot_weather + forty1 + 
##     vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + KC + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - JAC             1       0.0  3961.9 -53153
## - grass_1         1       0.1  3961.9 -53153
## - BUF             1       0.1  3962.0 -53153
## - hot_weather     1       0.1  3962.0 -53153
## - DET             1       0.2  3962.0 -53152
## - PIT             1       0.2  3962.0 -53152
## - STL             1       0.2  3962.1 -53152
## - CAR             1       0.2  3962.1 -53152
## - CIN             1       0.2  3962.1 -53152
## - OAK             1       0.3  3962.1 -53152
## <none>                         3961.9 -53151
## - ATL             1       0.4  3962.2 -53151
## - NYJ             1       0.4  3962.2 -53151
## - TEN             1       0.4  3962.3 -53151
## - CHI             1       0.5  3962.4 -53150
## - bad_weather_1   1       0.7  3962.6 -53149
## - WAS             1       0.7  3962.6 -53149
## - DEN             1       0.8  3962.6 -53148
## - IND             1       0.8  3962.6 -53148
## - PHI             1       0.8  3962.7 -53148
## - KC              1       0.8  3962.7 -53148
## - cold_weather    1       0.9  3962.8 -53147
## - TB              1       1.1  3962.9 -53146
## - MINN            1       1.1  3963.0 -53146
## - CLE             1       1.3  3963.2 -53145
## - HOU             1       1.3  3963.2 -53144
## - NOR             1       1.8  3963.6 -53141
## - NYG             1       2.3  3964.2 -53137
## - DAL             1       2.4  3964.2 -53137
## - avg_rbry_pos    1       3.1  3965.0 -53132
## - forty1          1       3.4  3965.3 -53130
## - SD              1       3.6  3965.5 -53129
## - vertical1       1       3.9  3965.7 -53127
## - avg_rectd_plyr  1       4.1  3966.0 -53125
## - NE              1       6.2  3968.0 -53111
## - GB              1       8.1  3970.0 -53097
## - weight          1       9.1  3971.0 -53090
## - avg_rbry_plyr   1      10.8  3972.6 -53079
## - height          1      17.4  3979.3 -53033
## - avg_fuml_plyr   1      79.8  4041.7 -52605
## - avg_qbtdp_plyr  1    7623.0 11584.9 -23663
## 
## Step:  AIC=-53153.32
## pc ~ height + weight + cold_weather + hot_weather + forty1 + 
##     vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - grass_1         1       0.1  3961.9 -53155
## - BUF             1       0.1  3962.0 -53155
## - hot_weather     1       0.1  3962.0 -53155
## - STL             1       0.2  3962.1 -53154
## - DET             1       0.2  3962.1 -53154
## - PIT             1       0.2  3962.1 -53154
## - CIN             1       0.3  3962.2 -53153
## - CAR             1       0.3  3962.2 -53153
## <none>                         3961.9 -53153
## - OAK             1       0.3  3962.2 -53153
## - ATL             1       0.4  3962.3 -53153
## - NYJ             1       0.4  3962.3 -53153
## - TEN             1       0.4  3962.3 -53152
## - CHI             1       0.6  3962.5 -53151
## - WAS             1       0.7  3962.6 -53150
## - bad_weather_1   1       0.7  3962.6 -53150
## - PHI             1       0.8  3962.7 -53150
## - KC              1       0.8  3962.7 -53150
## - DEN             1       0.8  3962.7 -53150
## - IND             1       0.8  3962.7 -53150
## - cold_weather    1       0.9  3962.8 -53149
## - MINN            1       1.1  3963.0 -53148
## - TB              1       1.1  3963.0 -53147
## - CLE             1       1.3  3963.2 -53146
## - HOU             1       1.3  3963.2 -53146
## - NOR             1       1.9  3963.8 -53142
## - NYG             1       2.4  3964.3 -53138
## - DAL             1       2.5  3964.4 -53138
## - avg_rbry_pos    1       3.1  3965.0 -53134
## - forty1          1       3.4  3965.3 -53132
## - SD              1       3.8  3965.7 -53129
## - vertical1       1       3.8  3965.7 -53129
## - avg_rectd_plyr  1       4.1  3966.0 -53127
## - NE              1       6.4  3968.3 -53111
## - GB              1       8.5  3970.4 -53096
## - weight          1       9.1  3971.0 -53092
## - avg_rbry_plyr   1      10.7  3972.6 -53081
## - height          1      17.4  3979.3 -53035
## - avg_fuml_plyr   1      79.8  4041.7 -52607
## - avg_qbtdp_plyr  1    7623.0 11584.9 -23665
## 
## Step:  AIC=-53154.92
## pc ~ height + weight + cold_weather + hot_weather + forty1 + 
##     vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BUF             1       0.1  3962.0 -53156
## - hot_weather     1       0.1  3962.1 -53156
## - DET             1       0.2  3962.1 -53156
## - STL             1       0.2  3962.1 -53156
## - PIT             1       0.2  3962.2 -53155
## - CIN             1       0.3  3962.2 -53155
## <none>                         3961.9 -53155
## - CAR             1       0.3  3962.2 -53155
## - OAK             1       0.3  3962.3 -53155
## - NYJ             1       0.4  3962.3 -53154
## - ATL             1       0.4  3962.3 -53154
## - TEN             1       0.5  3962.4 -53154
## - CHI             1       0.6  3962.6 -53153
## - WAS             1       0.7  3962.6 -53152
## - bad_weather_1   1       0.7  3962.7 -53152
## - PHI             1       0.8  3962.7 -53152
## - KC              1       0.8  3962.7 -53152
## - IND             1       0.8  3962.7 -53151
## - DEN             1       0.9  3962.8 -53151
## - cold_weather    1       1.0  3962.9 -53150
## - MINN            1       1.1  3963.1 -53149
## - TB              1       1.2  3963.1 -53149
## - CLE             1       1.2  3963.2 -53148
## - HOU             1       1.3  3963.3 -53148
## - NOR             1       1.8  3963.8 -53144
## - NYG             1       2.4  3964.3 -53140
## - DAL             1       2.4  3964.4 -53140
## - avg_rbry_pos    1       3.1  3965.1 -53135
## - forty1          1       3.4  3965.4 -53133
## - vertical1       1       3.8  3965.8 -53130
## - SD              1       3.9  3965.9 -53130
## - avg_rectd_plyr  1       4.1  3966.1 -53128
## - NE              1       6.4  3968.3 -53113
## - GB              1       8.6  3970.6 -53097
## - weight          1       9.1  3971.1 -53094
## - avg_rbry_plyr   1      10.8  3972.7 -53082
## - height          1      17.4  3979.3 -53037
## - avg_fuml_plyr   1      79.8  4041.7 -52609
## - avg_qbtdp_plyr  1    7623.0 11584.9 -23667
## 
## Step:  AIC=-53156.26
## pc ~ height + weight + cold_weather + hot_weather + forty1 + 
##     vertical1 + ATL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     GB + HOU + IND + KC + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + PIT + SD + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - hot_weather     1       0.1  3962.2 -53157
## - STL             1       0.2  3962.2 -53157
## - DET             1       0.2  3962.3 -53157
## - PIT             1       0.3  3962.3 -53156
## <none>                         3962.0 -53156
## - CIN             1       0.3  3962.3 -53156
## - CAR             1       0.4  3962.4 -53156
## - OAK             1       0.4  3962.4 -53156
## - ATL             1       0.4  3962.5 -53155
## - NYJ             1       0.4  3962.5 -53155
## - TEN             1       0.5  3962.6 -53154
## - WAS             1       0.6  3962.6 -53154
## - PHI             1       0.7  3962.7 -53153
## - KC              1       0.7  3962.8 -53153
## - bad_weather_1   1       0.7  3962.8 -53153
## - CHI             1       0.7  3962.8 -53153
## - IND             1       0.9  3962.9 -53152
## - cold_weather    1       0.9  3963.0 -53152
## - DEN             1       1.0  3963.0 -53151
## - MINN            1       1.0  3963.1 -53151
## - CLE             1       1.2  3963.2 -53150
## - HOU             1       1.3  3963.3 -53149
## - TB              1       1.3  3963.3 -53149
## - NOR             1       2.0  3964.1 -53144
## - NYG             1       2.6  3964.6 -53140
## - DAL             1       2.6  3964.7 -53140
## - avg_rbry_pos    1       3.2  3965.2 -53136
## - forty1          1       3.4  3965.4 -53135
## - vertical1       1       3.9  3966.0 -53131
## - avg_rectd_plyr  1       4.1  3966.2 -53130
## - SD              1       4.2  3966.2 -53129
## - NE              1       6.7  3968.7 -53112
## - GB              1       9.1  3971.1 -53095
## - weight          1       9.2  3971.2 -53095
## - avg_rbry_plyr   1      10.8  3972.8 -53084
## - height          1      17.6  3979.6 -53037
## - avg_fuml_plyr   1      80.0  4042.0 -52609
## - avg_qbtdp_plyr  1    7628.2 11590.3 -23657
## 
## Step:  AIC=-53157.45
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + 
##     KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - STL             1       0.2  3962.3 -53158
## - DET             1       0.2  3962.4 -53158
## - PIT             1       0.3  3962.4 -53157
## <none>                         3962.2 -53157
## - CIN             1       0.3  3962.5 -53157
## - CAR             1       0.4  3962.5 -53157
## - OAK             1       0.4  3962.5 -53157
## - ATL             1       0.4  3962.6 -53156
## - NYJ             1       0.5  3962.6 -53156
## - TEN             1       0.5  3962.7 -53156
## - WAS             1       0.6  3962.8 -53155
## - CHI             1       0.7  3962.9 -53155
## - bad_weather_1   1       0.7  3962.9 -53155
## - PHI             1       0.7  3962.9 -53155
## - KC              1       0.7  3962.9 -53154
## - IND             1       0.9  3963.0 -53153
## - cold_weather    1       0.9  3963.1 -53153
## - DEN             1       1.0  3963.1 -53153
## - MINN            1       1.0  3963.2 -53152
## - CLE             1       1.2  3963.3 -53151
## - HOU             1       1.3  3963.4 -53151
## - TB              1       1.3  3963.5 -53150
## - NOR             1       2.0  3964.2 -53145
## - NYG             1       2.6  3964.7 -53142
## - DAL             1       2.6  3964.8 -53141
## - avg_rbry_pos    1       3.2  3965.3 -53137
## - forty1          1       3.4  3965.5 -53136
## - vertical1       1       3.9  3966.1 -53132
## - avg_rectd_plyr  1       4.1  3966.3 -53131
## - SD              1       4.3  3966.4 -53130
## - NE              1       6.7  3968.8 -53113
## - GB              1       9.1  3971.2 -53097
## - weight          1       9.2  3971.3 -53096
## - avg_rbry_plyr   1      10.8  3972.9 -53085
## - height          1      17.6  3979.7 -53038
## - avg_fuml_plyr   1      80.0  4042.1 -52610
## - avg_qbtdp_plyr  1    7628.5 11590.6 -23658
## 
## Step:  AIC=-53158.35
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + 
##     KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - DET             1       0.3  3962.6 -53159
## <none>                         3962.3 -53158
## - PIT             1       0.3  3962.7 -53158
## - CIN             1       0.4  3962.7 -53158
## - CAR             1       0.4  3962.7 -53157
## - OAK             1       0.5  3962.8 -53157
## - ATL             1       0.5  3962.8 -53157
## - NYJ             1       0.5  3962.8 -53157
## - WAS             1       0.6  3962.9 -53157
## - TEN             1       0.6  3962.9 -53156
## - PHI             1       0.6  3963.0 -53156
## - KC              1       0.6  3963.0 -53156
## - bad_weather_1   1       0.7  3963.0 -53155
## - CHI             1       0.8  3963.1 -53155
## - cold_weather    1       0.9  3963.3 -53154
## - MINN            1       1.0  3963.3 -53154
## - IND             1       1.0  3963.3 -53153
## - CLE             1       1.1  3963.4 -53153
## - DEN             1       1.1  3963.4 -53153
## - HOU             1       1.2  3963.5 -53152
## - TB              1       1.5  3963.8 -53150
## - NOR             1       2.2  3964.5 -53145
## - NYG             1       2.8  3965.1 -53141
## - DAL             1       2.8  3965.1 -53141
## - avg_rbry_pos    1       3.2  3965.5 -53138
## - forty1          1       3.4  3965.7 -53137
## - vertical1       1       4.0  3966.3 -53133
## - avg_rectd_plyr  1       4.2  3966.5 -53131
## - SD              1       4.5  3966.9 -53129
## - NE              1       7.0  3969.3 -53112
## - weight          1       9.3  3971.6 -53096
## - GB              1       9.5  3971.8 -53095
## - avg_rbry_plyr   1      10.8  3973.1 -53085
## - height          1      17.6  3979.9 -53038
## - avg_fuml_plyr   1      80.2  4042.5 -52610
## - avg_qbtdp_plyr  1    7646.7 11609.0 -23616
## 
## Step:  AIC=-53158.56
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CAR + CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - PIT             1       0.3  3962.9 -53159
## <none>                         3962.6 -53159
## - CIN             1       0.3  3962.9 -53158
## - CAR             1       0.4  3962.9 -53158
## - OAK             1       0.4  3963.0 -53158
## - ATL             1       0.4  3963.0 -53158
## - NYJ             1       0.5  3963.0 -53157
## - TEN             1       0.6  3963.1 -53157
## - WAS             1       0.6  3963.2 -53156
## - CHI             1       0.7  3963.3 -53156
## - bad_weather_1   1       0.7  3963.3 -53155
## - PHI             1       0.7  3963.3 -53155
## - KC              1       0.7  3963.3 -53155
## - cold_weather    1       0.9  3963.5 -53154
## - IND             1       0.9  3963.5 -53154
## - DEN             1       1.0  3963.6 -53154
## - MINN            1       1.1  3963.7 -53153
## - CLE             1       1.2  3963.8 -53152
## - HOU             1       1.3  3963.9 -53151
## - TB              1       1.4  3963.9 -53151
## - NOR             1       2.0  3964.6 -53146
## - NYG             1       2.6  3965.2 -53142
## - DAL             1       2.7  3965.2 -53142
## - avg_rbry_pos    1       3.1  3965.7 -53139
## - forty1          1       3.4  3965.9 -53137
## - vertical1       1       4.1  3966.6 -53132
## - avg_rectd_plyr  1       4.3  3966.9 -53130
## - SD              1       4.4  3966.9 -53130
## - NE              1       6.8  3969.4 -53113
## - GB              1       9.3  3971.8 -53096
## - weight          1       9.3  3971.8 -53096
## - avg_rbry_plyr   1      10.7  3973.3 -53086
## - height          1      17.7  3980.2 -53038
## - avg_fuml_plyr   1      80.0  4042.6 -52611
## - avg_qbtdp_plyr  1    7646.5 11609.0 -23618
## 
## Step:  AIC=-53158.57
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CAR + CHI + CIN + CLE + DAL + DEN + GB + HOU + IND + KC + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - CIN             1       0.3  3963.1 -53159
## <none>                         3962.9 -53159
## - CAR             1       0.3  3963.2 -53159
## - OAK             1       0.3  3963.2 -53158
## - ATL             1       0.4  3963.2 -53158
## - NYJ             1       0.4  3963.2 -53158
## - TEN             1       0.5  3963.3 -53157
## - CHI             1       0.6  3963.5 -53156
## - WAS             1       0.7  3963.6 -53155
## - bad_weather_1   1       0.8  3963.6 -53155
## - IND             1       0.8  3963.7 -53155
## - PHI             1       0.8  3963.7 -53155
## - KC              1       0.9  3963.7 -53155
## - DEN             1       0.9  3963.8 -53154
## - cold_weather    1       1.0  3963.9 -53154
## - MINN            1       1.2  3964.1 -53152
## - TB              1       1.3  3964.1 -53152
## - CLE             1       1.4  3964.2 -53151
## - HOU             1       1.5  3964.3 -53150
## - NOR             1       1.9  3964.8 -53147
## - NYG             1       2.5  3965.3 -53143
## - DAL             1       2.5  3965.4 -53143
## - avg_rbry_pos    1       3.1  3965.9 -53139
## - forty1          1       3.4  3966.2 -53137
## - vertical1       1       4.1  3966.9 -53132
## - SD              1       4.2  3967.0 -53132
## - avg_rectd_plyr  1       4.4  3967.3 -53130
## - NE              1       6.6  3969.4 -53115
## - GB              1       9.0  3971.9 -53098
## - weight          1       9.2  3972.1 -53097
## - avg_rbry_plyr   1      10.7  3973.6 -53086
## - height          1      17.7  3980.5 -53038
## - avg_fuml_plyr   1      79.9  4042.7 -52612
## - avg_qbtdp_plyr  1    7646.4 11609.3 -23620
## 
## Step:  AIC=-53158.83
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CAR + CHI + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - CAR             1       0.2  3963.4 -53159
## - OAK             1       0.3  3963.4 -53159
## <none>                         3963.1 -53159
## - ATL             1       0.3  3963.4 -53159
## - NYJ             1       0.3  3963.4 -53159
## - TEN             1       0.4  3963.5 -53158
## - CHI             1       0.6  3963.7 -53157
## - IND             1       0.7  3963.8 -53156
## - bad_weather_1   1       0.8  3963.9 -53156
## - DEN             1       0.8  3963.9 -53155
## - WAS             1       0.8  3963.9 -53155
## - PHI             1       0.9  3964.0 -53154
## - KC              1       1.0  3964.1 -53154
## - cold_weather    1       1.0  3964.2 -53154
## - TB              1       1.2  3964.3 -53153
## - MINN            1       1.3  3964.4 -53152
## - CLE             1       1.5  3964.6 -53151
## - HOU             1       1.6  3964.7 -53150
## - NOR             1       1.8  3964.9 -53148
## - NYG             1       2.3  3965.5 -53145
## - DAL             1       2.4  3965.5 -53144
## - avg_rbry_pos    1       3.1  3966.2 -53139
## - forty1          1       3.3  3966.4 -53138
## - SD              1       4.0  3967.1 -53133
## - vertical1       1       4.0  3967.2 -53133
## - avg_rectd_plyr  1       4.4  3967.5 -53130
## - NE              1       6.4  3969.5 -53117
## - GB              1       8.8  3971.9 -53100
## - weight          1       9.1  3972.2 -53098
## - avg_rbry_plyr   1      10.8  3973.9 -53086
## - height          1      17.5  3980.7 -53039
## - avg_fuml_plyr   1      79.9  4043.1 -52612
## - avg_qbtdp_plyr  1    7648.3 11611.4 -23617
## 
## Step:  AIC=-53159.09
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CHI + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - OAK             1       0.2  3963.6 -53159
## - ATL             1       0.3  3963.6 -53159
## <none>                         3963.4 -53159
## - NYJ             1       0.3  3963.6 -53159
## - TEN             1       0.4  3963.7 -53159
## - CHI             1       0.5  3963.9 -53158
## - IND             1       0.7  3964.0 -53156
## - DEN             1       0.7  3964.1 -53156
## - bad_weather_1   1       0.8  3964.1 -53156
## - WAS             1       0.9  3964.3 -53155
## - PHI             1       1.0  3964.4 -53154
## - cold_weather    1       1.0  3964.4 -53154
## - KC              1       1.0  3964.4 -53154
## - TB              1       1.1  3964.4 -53154
## - MINN            1       1.4  3964.8 -53151
## - CLE             1       1.6  3964.9 -53150
## - NOR             1       1.7  3965.1 -53149
## - HOU             1       1.7  3965.1 -53149
## - NYG             1       2.2  3965.6 -53146
## - DAL             1       2.3  3965.6 -53145
## - avg_rbry_pos    1       3.2  3966.5 -53139
## - forty1          1       3.4  3966.7 -53138
## - SD              1       3.9  3967.3 -53134
## - vertical1       1       4.1  3967.4 -53133
## - avg_rectd_plyr  1       4.4  3967.7 -53131
## - NE              1       6.2  3969.6 -53118
## - GB              1       8.6  3972.0 -53101
## - weight          1       9.3  3972.6 -53097
## - avg_rbry_plyr   1      10.9  3974.3 -53086
## - height          1      17.7  3981.0 -53039
## - avg_fuml_plyr   1      79.9  4043.3 -52612
## - avg_qbtdp_plyr  1    7649.1 11612.4 -23616
## 
## Step:  AIC=-53159.45
## pc ~ height + weight + cold_weather + forty1 + vertical1 + ATL + 
##     CHI + CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + 
##     NOR + NYG + NYJ + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - ATL             1       0.2  3963.8 -53160
## - NYJ             1       0.3  3963.9 -53160
## <none>                         3963.6 -53159
## - TEN             1       0.3  3963.9 -53159
## - CHI             1       0.5  3964.1 -53158
## - IND             1       0.6  3964.2 -53157
## - DEN             1       0.7  3964.3 -53157
## - bad_weather_1   1       0.8  3964.4 -53156
## - cold_weather    1       1.0  3964.6 -53155
## - WAS             1       1.0  3964.6 -53155
## - TB              1       1.0  3964.6 -53154
## - PHI             1       1.1  3964.7 -53154
## - KC              1       1.1  3964.7 -53154
## - MINN            1       1.5  3965.1 -53151
## - NOR             1       1.6  3965.2 -53150
## - CLE             1       1.7  3965.3 -53150
## - HOU             1       1.8  3965.4 -53149
## - NYG             1       2.1  3965.7 -53147
## - DAL             1       2.2  3965.8 -53146
## - avg_rbry_pos    1       3.1  3966.7 -53140
## - forty1          1       3.5  3967.1 -53137
## - SD              1       3.8  3967.4 -53135
## - vertical1       1       4.0  3967.6 -53134
## - avg_rectd_plyr  1       4.3  3967.9 -53132
## - NE              1       6.1  3969.7 -53119
## - GB              1       8.5  3972.0 -53103
## - weight          1       9.2  3972.8 -53098
## - avg_rbry_plyr   1      10.8  3974.4 -53086
## - height          1      17.5  3981.1 -53041
## - avg_fuml_plyr   1      80.2  4043.8 -52611
## - avg_qbtdp_plyr  1    7648.9 11612.5 -23618
## 
## Step:  AIC=-53159.75
## pc ~ height + weight + cold_weather + forty1 + vertical1 + CHI + 
##     CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + NOR + 
##     NYG + NYJ + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - NYJ             1       0.2  3964.1 -53160
## <none>                         3963.8 -53160
## - TEN             1       0.3  3964.1 -53160
## - CHI             1       0.4  3964.3 -53159
## - IND             1       0.6  3964.4 -53158
## - DEN             1       0.6  3964.5 -53157
## - bad_weather_1   1       0.8  3964.6 -53156
## - cold_weather    1       0.9  3964.8 -53155
## - TB              1       0.9  3964.8 -53155
## - WAS             1       1.1  3964.9 -53154
## - PHI             1       1.2  3965.0 -53154
## - KC              1       1.2  3965.1 -53153
## - NOR             1       1.5  3965.4 -53151
## - MINN            1       1.6  3965.5 -53151
## - CLE             1       1.8  3965.6 -53149
## - HOU             1       2.0  3965.8 -53148
## - NYG             1       2.0  3965.9 -53148
## - DAL             1       2.1  3965.9 -53147
## - avg_rbry_pos    1       3.1  3966.9 -53141
## - forty1          1       3.5  3967.3 -53138
## - SD              1       3.7  3967.5 -53136
## - vertical1       1       3.9  3967.8 -53135
## - avg_rectd_plyr  1       4.5  3968.3 -53131
## - NE              1       5.9  3969.8 -53121
## - GB              1       8.3  3972.1 -53104
## - weight          1       9.2  3973.0 -53098
## - avg_rbry_plyr   1      10.9  3974.7 -53087
## - height          1      17.7  3981.5 -53040
## - avg_fuml_plyr   1      80.7  4044.6 -52607
## - avg_qbtdp_plyr  1    7659.4 11623.2 -23595
## 
## Step:  AIC=-53160.2
## pc ~ height + weight + cold_weather + forty1 + vertical1 + CHI + 
##     CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + NOR + 
##     NYG + PHI + SD + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - TEN             1       0.3  3964.3 -53160
## <none>                         3964.1 -53160
## - CHI             1       0.4  3964.5 -53160
## - IND             1       0.5  3964.6 -53159
## - DEN             1       0.6  3964.6 -53158
## - bad_weather_1   1       0.8  3964.8 -53157
## - TB              1       0.9  3965.0 -53156
## - cold_weather    1       1.0  3965.0 -53156
## - WAS             1       1.1  3965.2 -53154
## - PHI             1       1.3  3965.3 -53154
## - KC              1       1.3  3965.4 -53153
## - NOR             1       1.4  3965.5 -53152
## - MINN            1       1.7  3965.8 -53150
## - CLE             1       1.9  3965.9 -53149
## - NYG             1       2.0  3966.0 -53149
## - DAL             1       2.0  3966.1 -53148
## - HOU             1       2.1  3966.1 -53148
## - avg_rbry_pos    1       3.1  3967.2 -53141
## - forty1          1       3.4  3967.5 -53139
## - SD              1       3.6  3967.6 -53138
## - vertical1       1       4.1  3968.1 -53134
## - avg_rectd_plyr  1       4.4  3968.5 -53131
## - NE              1       5.8  3969.9 -53122
## - GB              1       8.1  3972.2 -53106
## - weight          1       9.2  3973.2 -53099
## - avg_rbry_plyr   1      10.9  3975.0 -53087
## - height          1      17.7  3981.7 -53040
## - avg_fuml_plyr   1      80.5  4044.6 -52609
## - avg_qbtdp_plyr  1    7669.1 11633.2 -23573
## 
## Step:  AIC=-53160.4
## pc ~ height + weight + cold_weather + forty1 + vertical1 + CHI + 
##     CLE + DAL + DEN + GB + HOU + IND + KC + MINN + NE + NOR + 
##     NYG + PHI + SD + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## <none>                         3964.3 -53160
## - CHI             1       0.4  3964.7 -53160
## - IND             1       0.5  3964.8 -53159
## - DEN             1       0.5  3964.9 -53159
## - bad_weather_1   1       0.7  3965.1 -53157
## - TB              1       0.8  3965.2 -53157
## - cold_weather    1       0.9  3965.3 -53156
## - WAS             1       1.2  3965.5 -53154
## - PHI             1       1.3  3965.7 -53153
## - KC              1       1.4  3965.7 -53153
## - NOR             1       1.4  3965.7 -53153
## - MINN            1       1.8  3966.1 -53150
## - NYG             1       1.9  3966.2 -53149
## - DAL             1       1.9  3966.2 -53149
## - CLE             1       2.0  3966.3 -53149
## - HOU             1       2.2  3966.5 -53147
## - avg_rbry_pos    1       3.1  3967.4 -53141
## - forty1          1       3.4  3967.7 -53139
## - SD              1       3.5  3967.8 -53138
## - vertical1       1       4.1  3968.4 -53134
## - avg_rectd_plyr  1       4.4  3968.7 -53132
## - NE              1       5.7  3970.0 -53123
## - GB              1       8.0  3972.3 -53107
## - weight          1       9.1  3973.5 -53099
## - avg_rbry_plyr   1      10.9  3975.2 -53087
## - height          1      17.6  3981.9 -53041
## - avg_fuml_plyr   1      80.4  4044.7 -52611
## - avg_qbtdp_plyr  1    7679.4 11643.7 -23550

Ints

PreProcess:

set.seed(123)
splitints <- sample.split(nfl_data$ints, SplitRatio = 0.7)
Trainints <- subset(nfl_data, split == TRUE)
Testints <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainints, method = c("center", "scale"))
trainTransformedints <- predict(preProcValues, Trainints)
testTransformedints <- predict(preProcValues, Testints)

ggpairs:

ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("ints",colnames(filtered_nfl_data_fields[46:51]))])

intsregform <- formula(paste("ints ~ ", 
                           paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegQBInts <- lm(intsregform, data = trainTransformedints)
summary(linRegQBInts) 
## 
## Call:
## lm(formula = intsregform, data = trainTransformedints)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8765 -0.0764 -0.0179  0.0449 10.8466 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -4.022e-15  4.798e-03   0.000 1.000000    
## height           5.147e-02  9.310e-03   5.529 3.26e-08 ***
## weight          -3.398e-02  8.725e-03  -3.894 9.88e-05 ***
## cold_weather     6.206e-03  5.051e-03   1.229 0.219163    
## hot_weather      1.959e-03  4.842e-03   0.404 0.685865    
## home_team_1     -6.020e-03  5.221e-03  -1.153 0.248898    
## forty1           3.365e-02  8.281e-03   4.063 4.85e-05 ***
## vertical1       -9.503e-03  6.367e-03  -1.493 0.135573    
## ARI              1.016e-02  6.712e-03   1.513 0.130288    
## ATL             -5.294e-03  6.744e-03  -0.785 0.432456    
## BAL              7.636e-03  6.750e-03   1.131 0.257943    
## BUF              8.200e-03  6.663e-03   1.231 0.218466    
## CAR              1.264e-02  6.620e-03   1.909 0.056221 .  
## CHI              1.153e-03  6.546e-03   0.176 0.860172    
## CIN              4.949e-03  6.667e-03   0.742 0.457881    
## CLE              1.330e-02  6.636e-03   2.004 0.045115 *  
## DAL             -4.229e-03  6.703e-03  -0.631 0.528103    
## DEN             -1.841e-03  6.728e-03  -0.274 0.784340    
## DET             -2.741e-03  6.636e-03  -0.413 0.679585    
## GB              -1.826e-02  6.832e-03  -2.672 0.007535 ** 
## HOU              9.650e-03  6.750e-03   1.430 0.152830    
## IND              5.421e-03  6.701e-03   0.809 0.418550    
## JAC              1.531e-02  6.537e-03   2.343 0.019147 *  
## KC               4.489e-04  6.680e-03   0.067 0.946424    
## MIA              2.154e-03  6.572e-03   0.328 0.743135    
## MINN             1.064e-02  6.613e-03   1.609 0.107730    
## NE              -2.341e-02  6.906e-03  -3.389 0.000701 ***
## NOR             -3.791e-03  6.885e-03  -0.551 0.581846    
## NYG              6.865e-04  6.729e-03   0.102 0.918749    
## NYJ              1.076e-02  6.704e-03   1.604 0.108674    
## OAK              1.077e-02  6.747e-03   1.597 0.110373    
## PHI              1.066e-02  6.538e-03   1.630 0.103015    
## PIT             -5.227e-03  6.709e-03  -0.779 0.435978    
## SD              -6.953e-03  6.584e-03  -1.056 0.290971    
## SEA              2.720e-03  6.833e-03   0.398 0.690581    
## STL              3.603e-03  6.651e-03   0.542 0.588043    
## TB               1.134e-03  6.588e-03   0.172 0.863375    
## TEN              5.676e-04  6.628e-03   0.086 0.931758    
## WAS              9.808e-03  6.663e-03   1.472 0.141046    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -2.067e-02  6.127e-03  -3.373 0.000743 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr   -5.063e-02  7.333e-03  -6.905 5.12e-12 ***
## avg_rbry_pos     2.058e-02  8.544e-03   2.409 0.016011 *  
## avg_fuml_plyr    1.376e-01  7.088e-03  19.418  < 2e-16 ***
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr   4.727e-01  7.699e-03  61.396  < 2e-16 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1          5.163e-04  5.521e-03   0.094 0.925497    
## bad_weather_1    8.351e-03  4.881e-03   1.711 0.087131 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7955 on 27438 degrees of freedom
## Multiple R-squared:  0.3682, Adjusted R-squared:  0.3672 
## F-statistic: 355.4 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegQBInts2 <- lm(ints ~ avg_qbints_plyr, data = trainTransformedints)

summary(linRegQBInts2)
## 
## Call:
## lm(formula = ints ~ avg_qbints_plyr, data = trainTransformedints)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0750 -0.0018 -0.0018 -0.0018 11.2261 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     -2.104e-15  4.606e-03     0.0        1    
## avg_qbints_plyr  6.457e-01  4.606e-03   140.2   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7636 on 27482 degrees of freedom
## Multiple R-squared:  0.417,  Adjusted R-squared:  0.4169 
## F-statistic: 1.965e+04 on 1 and 27482 DF,  p-value: < 2.2e-16

R2 of 0.4169, and really the only meaningful predictor was “how many interceptions have you thrown in the past”. Not an entirely amazing model, but at least we have something here.

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

PintPredicted <- predict(linRegQBInts2, newdata = testTransformedints)

SSEint <- sum((PintPredicted - testTransformedints$ints)^2)
SSTint <- sum((mean(nfl_data$ints)-testTransformedints$ints)^2)
r2_int <- 1 - SSEint/SSTint 
r2_int
## [1] 0.4500887
rmse_int <- sqrt(SSEint/nrow(testTransformedints))
rmse_int
## [1] 0.7879945

Regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBInts2, which = c(1:3,5))

Summary statistics:

confint(linRegQBInts2)
##                        2.5 %      97.5 %
## (Intercept)     -0.009027885 0.009027885
## avg_qbints_plyr  0.636692876 0.654748974
coef(summary(linRegQBInts2))
##                      Estimate  Std. Error       t value Pr(>|t|)
## (Intercept)     -2.104007e-15 0.004605945 -4.568024e-13        1
## avg_qbints_plyr  6.457209e-01 0.004606029  1.401904e+02        0
anova(linRegQBInts2)
## Analysis of Variance Table
## 
## Response: ints
##                    Df Sum Sq Mean Sq F value    Pr(>F)    
## avg_qbints_plyr     1  11459 11459.2   19653 < 2.2e-16 ***
## Residuals       27482  16024     0.6                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_ints <- step(lm(intsregform, data = trainTransformedints), direction = "backward")
## Start:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-12530.92
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - KC              1      0.00 17363 -12532.9
## - TEN             1      0.00 17363 -12532.9
## - grass_1         1      0.01 17363 -12532.9
## - NYG             1      0.01 17363 -12532.9
## - TB              1      0.02 17363 -12532.9
## - CHI             1      0.02 17363 -12532.9
## - DEN             1      0.05 17363 -12532.8
## - MIA             1      0.07 17363 -12532.8
## - SEA             1      0.10 17363 -12532.8
## - hot_weather     1      0.10 17363 -12532.8
## - DET             1      0.11 17363 -12532.7
## - STL             1      0.19 17363 -12532.6
## - NOR             1      0.19 17363 -12532.6
## - DAL             1      0.25 17363 -12532.5
## - CIN             1      0.35 17363 -12532.4
## - PIT             1      0.38 17363 -12532.3
## - ATL             1      0.39 17363 -12532.3
## - IND             1      0.41 17363 -12532.3
## - SD              1      0.71 17363 -12531.8
## - BAL             1      0.81 17364 -12531.6
## - home_team_1     1      0.84 17364 -12531.6
## - cold_weather    1      0.96 17364 -12531.4
## - BUF             1      0.96 17364 -12531.4
## <none>                        17363 -12530.9
## - HOU             1      1.29 17364 -12530.9
## - WAS             1      1.37 17364 -12530.7
## - vertical1       1      1.41 17364 -12530.7
## - ARI             1      1.45 17364 -12530.6
## - OAK             1      1.61 17364 -12530.4
## - NYJ             1      1.63 17364 -12530.3
## - MINN            1      1.64 17364 -12530.3
## - PHI             1      1.68 17364 -12530.3
## - bad_weather_1   1      1.85 17365 -12530.0
## - CAR             1      2.31 17365 -12529.3
## - CLE             1      2.54 17365 -12528.9
## - JAC             1      3.47 17366 -12527.4
## - avg_rbry_pos    1      3.67 17366 -12527.1
## - GB              1      4.52 17367 -12525.8
## - avg_rectd_plyr  1      7.20 17370 -12521.5
## - NE              1      7.27 17370 -12521.4
## - weight          1      9.60 17372 -12517.7
## - forty1          1     10.45 17373 -12516.4
## - height          1     19.34 17382 -12502.3
## - avg_rbry_plyr   1     30.17 17393 -12485.2
## - avg_fuml_plyr   1    238.61 17601 -12157.8
## - avg_qbtdp_plyr  1   2385.32 19748  -8994.9
## 
## Step:  AIC=-12532.91
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - TEN             1      0.00 17363 -12534.9
## - NYG             1      0.00 17363 -12534.9
## - grass_1         1      0.01 17363 -12534.9
## - TB              1      0.02 17363 -12534.9
## - CHI             1      0.02 17363 -12534.9
## - MIA             1      0.07 17363 -12534.8
## - DEN             1      0.08 17363 -12534.8
## - hot_weather     1      0.10 17363 -12534.7
## - SEA             1      0.11 17363 -12534.7
## - DET             1      0.16 17363 -12534.7
## - STL             1      0.21 17363 -12534.6
## - NOR             1      0.29 17363 -12534.5
## - DAL             1      0.36 17363 -12534.3
## - CIN             1      0.42 17363 -12534.3
## - IND             1      0.50 17363 -12534.1
## - ATL             1      0.55 17363 -12534.0
## - PIT             1      0.56 17363 -12534.0
## - home_team_1     1      0.84 17364 -12533.6
## - cold_weather    1      0.96 17364 -12533.4
## - SD              1      0.98 17364 -12533.4
## - BAL             1      1.01 17364 -12533.3
## - BUF             1      1.19 17364 -12533.0
## <none>                        17363 -12532.9
## - vertical1       1      1.41 17364 -12532.7
## - HOU             1      1.62 17364 -12532.4
## - WAS             1      1.74 17364 -12532.2
## - ARI             1      1.81 17365 -12532.0
## - bad_weather_1   1      1.85 17365 -12532.0
## - MINN            1      2.05 17365 -12531.7
## - NYJ             1      2.05 17365 -12531.7
## - OAK             1      2.06 17365 -12531.6
## - PHI             1      2.11 17365 -12531.6
## - CAR             1      2.94 17366 -12530.3
## - CLE             1      3.25 17366 -12529.8
## - avg_rbry_pos    1      3.68 17366 -12529.1
## - JAC             1      4.41 17367 -12527.9
## - GB              1      6.21 17369 -12525.1
## - avg_rectd_plyr  1      7.22 17370 -12523.5
## - weight          1      9.61 17372 -12519.7
## - NE              1      9.72 17372 -12519.5
## - forty1          1     10.45 17373 -12518.4
## - height          1     19.38 17382 -12504.3
## - avg_rbry_plyr   1     30.18 17393 -12487.2
## - avg_fuml_plyr   1    238.62 17601 -12159.8
## - avg_qbtdp_plyr  1   2386.52 19749  -8995.3
## 
## Step:  AIC=-12534.91
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - NYG             1      0.00 17363 -12536.9
## - grass_1         1      0.01 17363 -12536.9
## - TB              1      0.01 17363 -12536.9
## - CHI             1      0.01 17363 -12536.9
## - MIA             1      0.07 17363 -12536.8
## - DEN             1      0.10 17363 -12536.8
## - hot_weather     1      0.10 17363 -12536.7
## - SEA             1      0.11 17363 -12536.7
## - DET             1      0.19 17363 -12536.6
## - STL             1      0.22 17363 -12536.6
## - NOR             1      0.34 17363 -12536.4
## - DAL             1      0.42 17363 -12536.2
## - CIN             1      0.44 17363 -12536.2
## - IND             1      0.53 17363 -12536.1
## - ATL             1      0.64 17363 -12535.9
## - PIT             1      0.65 17363 -12535.9
## - home_team_1     1      0.84 17364 -12535.6
## - cold_weather    1      0.96 17364 -12535.4
## - BAL             1      1.10 17364 -12535.2
## - SD              1      1.13 17364 -12535.1
## <none>                        17363 -12534.9
## - BUF             1      1.28 17364 -12534.9
## - vertical1       1      1.41 17364 -12534.7
## - HOU             1      1.76 17364 -12534.1
## - bad_weather_1   1      1.85 17365 -12534.0
## - WAS             1      1.90 17365 -12533.9
## - ARI             1      1.97 17365 -12533.8
## - MINN            1      2.23 17365 -12533.4
## - NYJ             1      2.24 17365 -12533.4
## - OAK             1      2.27 17365 -12533.3
## - PHI             1      2.30 17365 -12533.3
## - CAR             1      3.23 17366 -12531.8
## - CLE             1      3.57 17366 -12531.3
## - avg_rbry_pos    1      3.68 17366 -12531.1
## - JAC             1      4.84 17368 -12529.3
## - GB              1      7.05 17370 -12525.8
## - avg_rectd_plyr  1      7.23 17370 -12525.5
## - weight          1      9.63 17372 -12521.7
## - forty1          1     10.45 17373 -12520.4
## - NE              1     10.92 17374 -12519.6
## - height          1     19.39 17382 -12506.2
## - avg_rbry_plyr   1     30.20 17393 -12489.1
## - avg_fuml_plyr   1    238.82 17602 -12161.5
## - avg_qbtdp_plyr  1   2387.65 19750  -8995.7
## 
## Step:  AIC=-12536.91
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - grass_1         1      0.00 17363 -12538.9
## - TB              1      0.01 17363 -12538.9
## - CHI             1      0.01 17363 -12538.9
## - MIA             1      0.07 17363 -12538.8
## - hot_weather     1      0.10 17363 -12538.7
## - SEA             1      0.11 17363 -12538.7
## - DEN             1      0.12 17363 -12538.7
## - DET             1      0.22 17363 -12538.6
## - STL             1      0.22 17363 -12538.6
## - NOR             1      0.39 17363 -12538.3
## - CIN             1      0.46 17363 -12538.2
## - DAL             1      0.47 17363 -12538.2
## - IND             1      0.55 17363 -12538.0
## - ATL             1      0.71 17363 -12537.8
## - PIT             1      0.72 17363 -12537.8
## - home_team_1     1      0.84 17364 -12537.6
## - cold_weather    1      0.97 17364 -12537.4
## - BAL             1      1.16 17364 -12537.1
## - SD              1      1.23 17364 -12537.0
## <none>                        17363 -12536.9
## - BUF             1      1.35 17364 -12536.8
## - vertical1       1      1.41 17364 -12536.7
## - HOU             1      1.85 17365 -12536.0
## - bad_weather_1   1      1.85 17365 -12536.0
## - WAS             1      1.98 17365 -12535.8
## - ARI             1      2.08 17365 -12535.6
## - MINN            1      2.35 17365 -12535.2
## - NYJ             1      2.37 17365 -12535.2
## - OAK             1      2.37 17365 -12535.2
## - PHI             1      2.41 17365 -12535.1
## - CAR             1      3.39 17366 -12533.5
## - avg_rbry_pos    1      3.69 17366 -12533.1
## - CLE             1      3.75 17366 -12533.0
## - JAC             1      5.07 17368 -12530.9
## - avg_rectd_plyr  1      7.23 17370 -12527.5
## - GB              1      7.66 17370 -12526.8
## - weight          1      9.63 17372 -12523.7
## - forty1          1     10.46 17373 -12522.4
## - NE              1     12.00 17375 -12519.9
## - height          1     19.40 17382 -12508.2
## - avg_rbry_plyr   1     30.22 17393 -12491.1
## - avg_fuml_plyr   1    238.82 17602 -12163.4
## - avg_qbtdp_plyr  1   2387.80 19751  -8997.5
## 
## Step:  AIC=-12538.9
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - TB              1      0.01 17363 -12540.9
## - CHI             1      0.01 17363 -12540.9
## - MIA             1      0.07 17363 -12540.8
## - hot_weather     1      0.11 17363 -12540.7
## - SEA             1      0.11 17363 -12540.7
## - DEN             1      0.11 17363 -12540.7
## - STL             1      0.22 17363 -12540.5
## - DET             1      0.23 17363 -12540.5
## - NOR             1      0.40 17363 -12540.3
## - CIN             1      0.45 17363 -12540.2
## - DAL             1      0.49 17363 -12540.1
## - IND             1      0.54 17363 -12540.0
## - PIT             1      0.71 17363 -12539.8
## - ATL             1      0.72 17363 -12539.8
## - home_team_1     1      0.84 17364 -12539.6
## - cold_weather    1      0.98 17364 -12539.3
## - BAL             1      1.15 17364 -12539.1
## - SD              1      1.22 17364 -12539.0
## <none>                        17363 -12538.9
## - BUF             1      1.35 17364 -12538.8
## - vertical1       1      1.41 17364 -12538.7
## - HOU             1      1.85 17365 -12538.0
## - bad_weather_1   1      1.86 17365 -12538.0
## - WAS             1      1.99 17365 -12537.7
## - ARI             1      2.08 17365 -12537.6
## - MINN            1      2.36 17365 -12537.2
## - NYJ             1      2.38 17365 -12537.1
## - OAK             1      2.40 17365 -12537.1
## - PHI             1      2.42 17365 -12537.1
## - CAR             1      3.40 17366 -12535.5
## - avg_rbry_pos    1      3.69 17366 -12535.1
## - CLE             1      3.77 17366 -12534.9
## - JAC             1      5.09 17368 -12532.8
## - avg_rectd_plyr  1      7.24 17370 -12529.4
## - GB              1      7.65 17370 -12528.8
## - weight          1      9.63 17372 -12525.7
## - forty1          1     10.46 17373 -12524.3
## - NE              1     12.31 17375 -12521.4
## - height          1     19.40 17382 -12510.2
## - avg_rbry_plyr   1     30.22 17393 -12493.1
## - avg_fuml_plyr   1    238.82 17602 -12165.4
## - avg_qbtdp_plyr  1   2387.94 19751  -8999.3
## 
## Step:  AIC=-12540.88
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - CHI             1      0.01 17363 -12542.9
## - MIA             1      0.06 17363 -12542.8
## - SEA             1      0.10 17363 -12542.7
## - hot_weather     1      0.11 17363 -12542.7
## - DEN             1      0.13 17363 -12542.7
## - STL             1      0.21 17363 -12542.5
## - DET             1      0.26 17363 -12542.5
## - CIN             1      0.44 17363 -12542.2
## - NOR             1      0.45 17363 -12542.2
## - IND             1      0.53 17363 -12542.0
## - DAL             1      0.54 17363 -12542.0
## - PIT             1      0.78 17364 -12541.6
## - ATL             1      0.79 17364 -12541.6
## - home_team_1     1      0.84 17364 -12541.6
## - cold_weather    1      0.97 17364 -12541.3
## - BAL             1      1.15 17364 -12541.1
## <none>                        17363 -12540.9
## - SD              1      1.32 17364 -12540.8
## - BUF             1      1.35 17364 -12540.7
## - vertical1       1      1.42 17364 -12540.6
## - bad_weather_1   1      1.86 17365 -12539.9
## - HOU             1      1.86 17365 -12539.9
## - WAS             1      2.01 17365 -12539.7
## - ARI             1      2.10 17365 -12539.6
## - MINN            1      2.38 17365 -12539.1
## - NYJ             1      2.41 17365 -12539.1
## - OAK             1      2.43 17365 -12539.0
## - PHI             1      2.44 17365 -12539.0
## - CAR             1      3.45 17366 -12537.4
## - avg_rbry_pos    1      3.69 17366 -12537.0
## - CLE             1      3.82 17367 -12536.8
## - JAC             1      5.18 17368 -12534.7
## - avg_rectd_plyr  1      7.24 17370 -12531.4
## - GB              1      8.08 17371 -12530.1
## - weight          1      9.62 17372 -12527.7
## - forty1          1     10.45 17373 -12526.3
## - NE              1     12.93 17376 -12522.4
## - height          1     19.40 17382 -12512.2
## - avg_rbry_plyr   1     30.23 17393 -12495.1
## - avg_fuml_plyr   1    238.88 17602 -12167.3
## - avg_qbtdp_plyr  1   2387.94 19751  -9001.2
## 
## Step:  AIC=-12542.86
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + 
##     NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - MIA             1      0.06 17363 -12545
## - SEA             1      0.09 17363 -12545
## - hot_weather     1      0.11 17363 -12545
## - DEN             1      0.15 17363 -12545
## - STL             1      0.20 17363 -12544
## - DET             1      0.28 17363 -12544
## - CIN             1      0.43 17363 -12544
## - NOR             1      0.48 17363 -12544
## - IND             1      0.52 17363 -12544
## - DAL             1      0.58 17363 -12544
## - PIT             1      0.83 17364 -12544
## - ATL             1      0.84 17364 -12544
## - home_team_1     1      0.84 17364 -12544
## - cold_weather    1      0.98 17364 -12543
## - BAL             1      1.15 17364 -12543
## <none>                        17363 -12543
## - BUF             1      1.35 17364 -12543
## - SD              1      1.39 17364 -12543
## - vertical1       1      1.43 17364 -12543
## - bad_weather_1   1      1.87 17365 -12542
## - HOU             1      1.87 17365 -12542
## - WAS             1      2.01 17365 -12542
## - ARI             1      2.11 17365 -12542
## - MINN            1      2.39 17365 -12541
## - NYJ             1      2.42 17365 -12541
## - OAK             1      2.44 17365 -12541
## - PHI             1      2.45 17365 -12541
## - CAR             1      3.48 17366 -12539
## - avg_rbry_pos    1      3.69 17366 -12539
## - CLE             1      3.86 17367 -12539
## - JAC             1      5.23 17368 -12537
## - avg_rectd_plyr  1      7.24 17370 -12533
## - GB              1      8.41 17371 -12532
## - weight          1      9.65 17372 -12530
## - forty1          1     10.44 17373 -12528
## - NE              1     13.38 17376 -12524
## - height          1     19.48 17382 -12514
## - avg_rbry_plyr   1     30.23 17393 -12497
## - avg_fuml_plyr   1    239.10 17602 -12169
## - avg_qbtdp_plyr  1   2388.79 19752  -9002
## 
## Step:  AIC=-12544.78
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + 
##     NOR + NYJ + OAK + PHI + PIT + SD + SEA + STL + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - SEA             1      0.07 17363 -12546.7
## - hot_weather     1      0.11 17363 -12546.6
## - STL             1      0.18 17363 -12546.5
## - DEN             1      0.18 17363 -12546.5
## - DET             1      0.32 17363 -12546.3
## - CIN             1      0.40 17363 -12546.1
## - IND             1      0.49 17363 -12546.0
## - NOR             1      0.54 17363 -12545.9
## - DAL             1      0.64 17363 -12545.8
## - home_team_1     1      0.84 17364 -12545.4
## - PIT             1      0.91 17364 -12545.3
## - ATL             1      0.92 17364 -12545.3
## - cold_weather    1      0.97 17364 -12545.2
## - BAL             1      1.10 17364 -12545.0
## <none>                        17363 -12544.8
## - BUF             1      1.30 17364 -12544.7
## - vertical1       1      1.44 17364 -12544.5
## - SD              1      1.49 17364 -12544.4
## - HOU             1      1.82 17365 -12543.9
## - bad_weather_1   1      1.86 17365 -12543.8
## - WAS             1      1.96 17365 -12543.7
## - ARI             1      2.05 17365 -12543.5
## - MINN            1      2.33 17365 -12543.1
## - NYJ             1      2.37 17365 -12543.0
## - OAK             1      2.39 17365 -12543.0
## - PHI             1      2.40 17365 -12543.0
## - CAR             1      3.43 17366 -12541.3
## - avg_rbry_pos    1      3.71 17367 -12540.9
## - CLE             1      3.81 17367 -12540.8
## - JAC             1      5.18 17368 -12538.6
## - avg_rectd_plyr  1      7.22 17370 -12535.4
## - GB              1      8.80 17372 -12532.9
## - weight          1      9.65 17372 -12531.5
## - forty1          1     10.43 17373 -12530.3
## - NE              1     13.92 17377 -12524.7
## - height          1     19.47 17382 -12516.0
## - avg_rbry_plyr   1     30.29 17393 -12498.9
## - avg_fuml_plyr   1    239.12 17602 -12170.8
## - avg_qbtdp_plyr  1   2388.80 19752  -9003.9
## 
## Step:  AIC=-12546.66
## ints ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + 
##     NOR + NYJ + OAK + PHI + PIT + SD + STL + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - hot_weather     1      0.12 17363 -12548.5
## - STL             1      0.15 17363 -12548.4
## - DEN             1      0.22 17363 -12548.3
## - CIN             1      0.36 17363 -12548.1
## - DET             1      0.37 17363 -12548.1
## - IND             1      0.45 17363 -12548.0
## - NOR             1      0.61 17363 -12547.7
## - DAL             1      0.71 17364 -12547.5
## - home_team_1     1      0.84 17364 -12547.3
## - PIT             1      1.00 17364 -12547.1
## - cold_weather    1      1.00 17364 -12547.1
## - ATL             1      1.00 17364 -12547.1
## - BAL             1      1.04 17364 -12547.0
## - BUF             1      1.24 17364 -12546.7
## <none>                        17363 -12546.7
## - vertical1       1      1.43 17364 -12546.4
## - SD              1      1.60 17364 -12546.1
## - HOU             1      1.75 17365 -12545.9
## - bad_weather_1   1      1.86 17365 -12545.7
## - WAS             1      1.89 17365 -12545.7
## - ARI             1      1.99 17365 -12545.5
## - MINN            1      2.27 17365 -12545.1
## - NYJ             1      2.30 17365 -12545.0
## - OAK             1      2.32 17365 -12545.0
## - PHI             1      2.33 17365 -12545.0
## - CAR             1      3.36 17366 -12543.3
## - avg_rbry_pos    1      3.68 17367 -12542.8
## - CLE             1      3.73 17367 -12542.8
## - JAC             1      5.11 17368 -12540.6
## - avg_rectd_plyr  1      7.20 17370 -12537.3
## - GB              1      9.22 17372 -12534.1
## - weight          1      9.61 17372 -12533.5
## - forty1          1     10.41 17373 -12532.2
## - NE              1     14.49 17377 -12525.7
## - height          1     19.40 17382 -12518.0
## - avg_rbry_plyr   1     30.22 17393 -12500.9
## - avg_fuml_plyr   1    239.38 17602 -12172.3
## - avg_qbtdp_plyr  1   2400.61 19763  -8989.4
## 
## Step:  AIC=-12548.47
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYJ + 
##     OAK + PHI + PIT + SD + STL + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - STL             1      0.16 17363 -12550.2
## - DEN             1      0.21 17363 -12550.1
## - CIN             1      0.36 17363 -12549.9
## - DET             1      0.37 17363 -12549.9
## - IND             1      0.44 17363 -12549.8
## - NOR             1      0.61 17364 -12549.5
## - DAL             1      0.72 17364 -12549.3
## - home_team_1     1      0.84 17364 -12549.1
## - cold_weather    1      0.98 17364 -12548.9
## - PIT             1      0.99 17364 -12548.9
## - ATL             1      1.01 17364 -12548.9
## - BAL             1      1.03 17364 -12548.8
## - BUF             1      1.26 17364 -12548.5
## <none>                        17363 -12548.5
## - vertical1       1      1.43 17364 -12548.2
## - SD              1      1.57 17365 -12548.0
## - HOU             1      1.74 17365 -12547.7
## - bad_weather_1   1      1.85 17365 -12547.5
## - WAS             1      1.88 17365 -12547.5
## - ARI             1      1.97 17365 -12547.3
## - MINN            1      2.26 17365 -12546.9
## - OAK             1      2.31 17365 -12546.8
## - PHI             1      2.32 17365 -12546.8
## - NYJ             1      2.32 17365 -12546.8
## - CAR             1      3.34 17366 -12545.2
## - avg_rbry_pos    1      3.67 17367 -12544.7
## - CLE             1      3.72 17367 -12544.6
## - JAC             1      5.09 17368 -12542.4
## - avg_rectd_plyr  1      7.20 17370 -12539.1
## - GB              1      9.24 17372 -12535.9
## - weight          1      9.63 17373 -12535.2
## - forty1          1     10.41 17373 -12534.0
## - NE              1     14.52 17378 -12527.5
## - height          1     19.42 17382 -12519.8
## - avg_rbry_plyr   1     30.19 17393 -12502.7
## - avg_fuml_plyr   1    239.37 17602 -12174.2
## - avg_qbtdp_plyr  1   2400.57 19764  -8991.3
## 
## Step:  AIC=-12550.23
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYJ + 
##     OAK + PHI + PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - DEN             1      0.26 17363 -12551.8
## - CIN             1      0.31 17363 -12551.7
## - IND             1      0.38 17364 -12551.6
## - DET             1      0.44 17364 -12551.5
## - NOR             1      0.69 17364 -12551.1
## - DAL             1      0.82 17364 -12550.9
## - BAL             1      0.96 17364 -12550.7
## - cold_weather    1      0.96 17364 -12550.7
## - home_team_1     1      0.96 17364 -12550.7
## - PIT             1      1.09 17364 -12550.5
## - ATL             1      1.14 17364 -12550.4
## - BUF             1      1.18 17364 -12550.4
## <none>                        17363 -12550.2
## - vertical1       1      1.46 17365 -12549.9
## - HOU             1      1.63 17365 -12549.6
## - SD              1      1.69 17365 -12549.5
## - WAS             1      1.79 17365 -12549.4
## - bad_weather_1   1      1.82 17365 -12549.3
## - ARI             1      1.86 17365 -12549.3
## - MINN            1      2.15 17365 -12548.8
## - OAK             1      2.20 17365 -12548.7
## - PHI             1      2.22 17365 -12548.7
## - NYJ             1      2.22 17365 -12548.7
## - CAR             1      3.23 17366 -12547.1
## - CLE             1      3.60 17367 -12546.5
## - avg_rbry_pos    1      3.66 17367 -12546.4
## - JAC             1      4.96 17368 -12544.4
## - avg_rectd_plyr  1      7.29 17370 -12540.7
## - GB              1      9.59 17373 -12537.0
## - weight          1      9.70 17373 -12536.9
## - forty1          1     10.46 17374 -12535.7
## - NE              1     15.00 17378 -12528.5
## - height          1     19.46 17383 -12521.4
## - avg_rbry_plyr   1     30.27 17393 -12504.4
## - avg_fuml_plyr   1    239.56 17603 -12175.6
## - avg_qbtdp_plyr  1   2403.30 19766  -8989.3
## 
## Step:  AIC=-12551.82
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CIN + CLE + DAL + 
##     DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYJ + OAK + 
##     PHI + PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - CIN             1      0.38 17364 -12553.2
## - DET             1      0.38 17364 -12553.2
## - IND             1      0.46 17364 -12553.1
## - NOR             1      0.61 17364 -12552.8
## - DAL             1      0.74 17364 -12552.7
## - cold_weather    1      0.93 17364 -12552.3
## - PIT             1      0.99 17364 -12552.3
## - home_team_1     1      1.00 17364 -12552.2
## - ATL             1      1.05 17364 -12552.2
## - BAL             1      1.08 17364 -12552.1
## <none>                        17363 -12551.8
## - BUF             1      1.31 17365 -12551.8
## - vertical1       1      1.52 17365 -12551.4
## - SD              1      1.58 17365 -12551.3
## - HOU             1      1.77 17365 -12551.0
## - bad_weather_1   1      1.85 17365 -12550.9
## - WAS             1      1.96 17365 -12550.7
## - ARI             1      2.01 17365 -12550.6
## - MINN            1      2.32 17366 -12550.1
## - OAK             1      2.38 17366 -12550.1
## - PHI             1      2.40 17366 -12550.0
## - NYJ             1      2.41 17366 -12550.0
## - CAR             1      3.45 17367 -12548.4
## - avg_rbry_pos    1      3.65 17367 -12548.0
## - CLE             1      3.84 17367 -12547.7
## - JAC             1      5.25 17369 -12545.5
## - avg_rectd_plyr  1      7.45 17371 -12542.0
## - GB              1      9.36 17373 -12539.0
## - weight          1      9.71 17373 -12538.5
## - forty1          1     10.39 17374 -12537.4
## - NE              1     14.75 17378 -12530.5
## - height          1     19.60 17383 -12522.8
## - avg_rbry_plyr   1     30.25 17394 -12506.0
## - avg_fuml_plyr   1    239.46 17603 -12177.4
## - avg_qbtdp_plyr  1   2403.64 19767  -8990.5
## 
## Step:  AIC=-12553.22
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + DET + 
##     GB + HOU + IND + JAC + MINN + NE + NOR + NYJ + OAK + PHI + 
##     PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - IND             1      0.39 17364 -12554.6
## - DET             1      0.45 17364 -12554.5
## - NOR             1      0.71 17364 -12554.1
## - DAL             1      0.84 17365 -12553.9
## - BAL             1      0.97 17365 -12553.7
## - cold_weather    1      0.98 17365 -12553.7
## - home_team_1     1      0.99 17365 -12553.7
## - PIT             1      1.11 17365 -12553.5
## - ATL             1      1.17 17365 -12553.4
## - BUF             1      1.19 17365 -12553.3
## <none>                        17364 -12553.2
## - vertical1       1      1.53 17365 -12552.8
## - HOU             1      1.65 17365 -12552.6
## - SD              1      1.73 17366 -12552.5
## - WAS             1      1.83 17366 -12552.3
## - bad_weather_1   1      1.87 17366 -12552.3
## - ARI             1      1.88 17366 -12552.2
## - MINN            1      2.18 17366 -12551.8
## - OAK             1      2.23 17366 -12551.7
## - PHI             1      2.25 17366 -12551.7
## - NYJ             1      2.26 17366 -12551.6
## - CAR             1      3.28 17367 -12550.0
## - avg_rbry_pos    1      3.66 17367 -12549.4
## - CLE             1      3.66 17367 -12549.4
## - JAC             1      5.05 17369 -12547.2
## - avg_rectd_plyr  1      7.46 17371 -12543.4
## - GB              1      9.81 17374 -12539.7
## - weight          1      9.88 17374 -12539.6
## - forty1          1     10.48 17374 -12538.6
## - NE              1     15.35 17379 -12530.9
## - height          1     19.76 17384 -12524.0
## - avg_rbry_plyr   1     30.14 17394 -12507.6
## - avg_fuml_plyr   1    239.26 17603 -12179.1
## - avg_qbtdp_plyr  1   2403.48 19767  -8992.2
## 
## Step:  AIC=-12554.6
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + DET + 
##     GB + HOU + JAC + MINN + NE + NOR + NYJ + OAK + PHI + PIT + 
##     SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - DET             1      0.54 17365 -12555.8
## - NOR             1      0.83 17365 -12555.3
## - BAL             1      0.88 17365 -12555.2
## - cold_weather    1      0.95 17365 -12555.1
## - DAL             1      0.97 17365 -12555.1
## - BUF             1      1.09 17365 -12554.9
## - home_team_1     1      1.16 17365 -12554.8
## - PIT             1      1.23 17365 -12554.7
## <none>                        17364 -12554.6
## - ATL             1      1.32 17365 -12554.5
## - vertical1       1      1.49 17366 -12554.3
## - HOU             1      1.51 17366 -12554.2
## - WAS             1      1.70 17366 -12553.9
## - ARI             1      1.73 17366 -12553.9
## - bad_weather_1   1      1.86 17366 -12553.7
## - SD              1      1.87 17366 -12553.6
## - MINN            1      2.04 17366 -12553.4
## - OAK             1      2.09 17366 -12553.3
## - PHI             1      2.12 17366 -12553.3
## - NYJ             1      2.12 17366 -12553.2
## - CAR             1      3.12 17367 -12551.7
## - CLE             1      3.50 17368 -12551.1
## - avg_rbry_pos    1      3.61 17368 -12550.9
## - JAC             1      4.85 17369 -12548.9
## - avg_rectd_plyr  1      7.39 17372 -12544.9
## - weight          1      9.74 17374 -12541.2
## - GB              1     10.23 17374 -12540.4
## - forty1          1     10.43 17375 -12540.1
## - NE              1     15.86 17380 -12531.5
## - height          1     19.54 17384 -12525.7
## - avg_rbry_plyr   1     30.13 17394 -12509.0
## - avg_fuml_plyr   1    239.12 17603 -12180.7
## - avg_qbtdp_plyr  1   2411.73 19776  -8982.2
## 
## Step:  AIC=-12555.75
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + GB + 
##     HOU + JAC + MINN + NE + NOR + NYJ + OAK + PHI + PIT + SD + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - NOR             1      0.71 17365 -12556.6
## - DAL             1      0.85 17366 -12556.4
## - BAL             1      0.99 17366 -12556.2
## - home_team_1     1      1.03 17366 -12556.1
## - cold_weather    1      1.05 17366 -12556.1
## - PIT             1      1.13 17366 -12556.0
## - ATL             1      1.18 17366 -12555.9
## - BUF             1      1.21 17366 -12555.8
## <none>                        17365 -12555.8
## - vertical1       1      1.57 17366 -12555.3
## - HOU             1      1.69 17366 -12555.1
## - SD              1      1.73 17366 -12555.0
## - WAS             1      1.85 17367 -12554.8
## - bad_weather_1   1      1.85 17367 -12554.8
## - ARI             1      1.92 17367 -12554.7
## - MINN            1      2.21 17367 -12554.3
## - OAK             1      2.27 17367 -12554.2
## - PHI             1      2.28 17367 -12554.1
## - NYJ             1      2.30 17367 -12554.1
## - CAR             1      3.33 17368 -12552.5
## - avg_rbry_pos    1      3.50 17368 -12552.2
## - CLE             1      3.70 17368 -12551.9
## - JAC             1      5.13 17370 -12549.6
## - avg_rectd_plyr  1      7.62 17372 -12545.7
## - weight          1      9.77 17374 -12542.3
## - GB              1      9.94 17375 -12542.0
## - forty1          1     10.33 17375 -12541.4
## - NE              1     15.52 17380 -12533.2
## - height          1     19.59 17384 -12526.8
## - avg_rbry_plyr   1     29.89 17395 -12510.5
## - avg_fuml_plyr   1    238.84 17604 -12182.3
## - avg_qbtdp_plyr  1   2411.25 19776  -8984.1
## 
## Step:  AIC=-12556.62
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + DAL + GB + 
##     HOU + JAC + MINN + NE + NYJ + OAK + PHI + PIT + SD + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - DAL             1      0.72 17366 -12557.5
## - home_team_1     1      0.92 17366 -12557.2
## - PIT             1      1.01 17366 -12557.0
## - ATL             1      1.02 17366 -12557.0
## - BAL             1      1.12 17367 -12556.8
## - cold_weather    1      1.13 17367 -12556.8
## <none>                        17365 -12556.6
## - BUF             1      1.35 17367 -12556.5
## - vertical1       1      1.57 17367 -12556.1
## - SD              1      1.58 17367 -12556.1
## - bad_weather_1   1      1.83 17367 -12555.7
## - HOU             1      1.89 17367 -12555.6
## - WAS             1      2.02 17367 -12555.4
## - ARI             1      2.13 17368 -12555.2
## - MINN            1      2.38 17368 -12554.8
## - PHI             1      2.46 17368 -12554.7
## - OAK             1      2.48 17368 -12554.7
## - NYJ             1      2.48 17368 -12554.7
## - avg_rbry_pos    1      3.33 17369 -12553.4
## - CAR             1      3.57 17369 -12553.0
## - CLE             1      3.91 17369 -12552.4
## - JAC             1      5.44 17371 -12550.0
## - avg_rectd_plyr  1      8.14 17374 -12545.7
## - GB              1      9.56 17375 -12543.5
## - weight          1      9.82 17375 -12543.1
## - forty1          1     10.42 17376 -12542.1
## - NE              1     15.07 17380 -12534.8
## - height          1     19.69 17385 -12527.5
## - avg_rbry_plyr   1     29.73 17395 -12511.6
## - avg_fuml_plyr   1    240.61 17606 -12180.4
## - avg_qbtdp_plyr  1   2420.52 19786  -8972.2
## 
## Step:  AIC=-12557.49
## ints ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CLE + GB + HOU + 
##     JAC + MINN + NE + NYJ + OAK + PHI + PIT + SD + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - home_team_1     1      0.74 17367 -12558.3
## - ATL             1      0.89 17367 -12558.1
## - PIT             1      0.91 17367 -12558.0
## - cold_weather    1      1.19 17367 -12557.6
## - BAL             1      1.24 17367 -12557.5
## <none>                        17366 -12557.5
## - SD              1      1.45 17368 -12557.2
## - BUF             1      1.47 17368 -12557.2
## - vertical1       1      1.55 17368 -12557.0
## - bad_weather_1   1      1.82 17368 -12556.6
## - HOU             1      2.10 17368 -12556.2
## - WAS             1      2.17 17368 -12556.1
## - ARI             1      2.35 17368 -12555.8
## - MINN            1      2.56 17369 -12555.4
## - PHI             1      2.63 17369 -12555.3
## - NYJ             1      2.65 17369 -12555.3
## - OAK             1      2.67 17369 -12555.3
## - avg_rbry_pos    1      3.32 17369 -12554.2
## - CAR             1      3.78 17370 -12553.5
## - CLE             1      4.10 17370 -12553.0
## - JAC             1      5.70 17372 -12550.5
## - avg_rectd_plyr  1      8.34 17374 -12546.3
## - GB              1      9.26 17375 -12544.8
## - weight          1      9.76 17376 -12544.0
## - forty1          1     10.40 17377 -12543.0
## - NE              1     14.71 17381 -12536.2
## - height          1     19.64 17386 -12528.4
## - avg_rbry_plyr   1     29.91 17396 -12512.2
## - avg_fuml_plyr   1    240.97 17607 -12180.7
## - avg_qbtdp_plyr  1   2419.81 19786  -8974.2
## 
## Step:  AIC=-12558.32
## ints ~ height + weight + cold_weather + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CLE + GB + HOU + JAC + MINN + 
##     NE + NYJ + OAK + PHI + PIT + SD + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - ATL             1      0.72 17368 -12559.2
## - PIT             1      0.98 17368 -12558.8
## - cold_weather    1      1.03 17368 -12558.7
## - BAL             1      1.17 17368 -12558.5
## <none>                        17367 -12558.3
## - BUF             1      1.42 17368 -12558.1
## - vertical1       1      1.55 17368 -12557.9
## - SD              1      1.55 17368 -12557.9
## - bad_weather_1   1      1.75 17369 -12557.6
## - WAS             1      2.05 17369 -12557.1
## - HOU             1      2.43 17369 -12556.5
## - PHI             1      2.53 17369 -12556.3
## - MINN            1      2.54 17369 -12556.3
## - OAK             1      2.56 17369 -12556.3
## - NYJ             1      2.56 17369 -12556.3
## - ARI             1      2.70 17370 -12556.0
## - avg_rbry_pos    1      3.34 17370 -12555.0
## - CAR             1      3.63 17371 -12554.6
## - CLE             1      3.96 17371 -12554.0
## - JAC             1      5.52 17372 -12551.6
## - avg_rectd_plyr  1      8.27 17375 -12547.2
## - GB              1      9.47 17376 -12545.3
## - weight          1      9.76 17377 -12544.9
## - forty1          1     10.43 17377 -12543.8
## - NE              1     15.05 17382 -12536.5
## - height          1     19.60 17386 -12529.3
## - avg_rbry_plyr   1     29.92 17397 -12513.0
## - avg_fuml_plyr   1    240.75 17608 -12181.9
## - avg_qbtdp_plyr  1   2421.14 19788  -8973.3
## 
## Step:  AIC=-12559.17
## ints ~ height + weight + cold_weather + forty1 + vertical1 + 
##     ARI + BAL + BUF + CAR + CLE + GB + HOU + JAC + MINN + NE + 
##     NYJ + OAK + PHI + PIT + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - PIT             1      0.89 17368 -12559.8
## - cold_weather    1      1.17 17369 -12559.3
## <none>                        17368 -12559.2
## - BAL             1      1.28 17369 -12559.1
## - SD              1      1.42 17369 -12558.9
## - vertical1       1      1.45 17369 -12558.9
## - BUF             1      1.54 17369 -12558.7
## - bad_weather_1   1      1.77 17369 -12558.4
## - WAS             1      2.20 17370 -12557.7
## - HOU             1      2.62 17370 -12557.0
## - MINN            1      2.68 17370 -12556.9
## - PHI             1      2.70 17370 -12556.9
## - NYJ             1      2.71 17370 -12556.9
## - OAK             1      2.74 17370 -12556.8
## - ARI             1      2.88 17370 -12556.6
## - avg_rbry_pos    1      3.30 17371 -12556.0
## - CAR             1      3.84 17371 -12555.1
## - CLE             1      4.14 17372 -12554.6
## - JAC             1      5.79 17373 -12552.0
## - avg_rectd_plyr  1      8.55 17376 -12547.6
## - GB              1      9.17 17377 -12546.7
## - weight          1      9.79 17377 -12545.7
## - forty1          1     10.39 17378 -12544.7
## - NE              1     14.65 17382 -12538.0
## - height          1     19.88 17387 -12529.7
## - avg_rbry_plyr   1     29.95 17398 -12513.8
## - avg_fuml_plyr   1    242.63 17610 -12179.9
## - avg_qbtdp_plyr  1   2421.52 19789  -8973.8
## 
## Step:  AIC=-12559.76
## ints ~ height + weight + cold_weather + forty1 + vertical1 + 
##     ARI + BAL + BUF + CAR + CLE + GB + HOU + JAC + MINN + NE + 
##     NYJ + OAK + PHI + SD + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - cold_weather    1      0.99 17369 -12560.2
## <none>                        17368 -12559.8
## - SD              1      1.31 17370 -12559.7
## - BAL             1      1.43 17370 -12559.5
## - vertical1       1      1.44 17370 -12559.5
## - BUF             1      1.70 17370 -12559.1
## - bad_weather_1   1      1.73 17370 -12559.0
## - WAS             1      2.39 17371 -12558.0
## - HOU             1      2.79 17371 -12557.3
## - MINN            1      2.88 17371 -12557.2
## - PHI             1      2.90 17371 -12557.2
## - NYJ             1      2.93 17371 -12557.1
## - OAK             1      2.93 17371 -12557.1
## - ARI             1      3.08 17372 -12556.9
## - avg_rbry_pos    1      3.29 17372 -12556.6
## - CAR             1      4.08 17373 -12555.3
## - CLE             1      4.42 17373 -12554.8
## - JAC             1      6.04 17375 -12552.2
## - avg_rectd_plyr  1      8.64 17377 -12548.1
## - GB              1      8.81 17377 -12547.8
## - weight          1      9.79 17378 -12546.3
## - forty1          1     10.41 17379 -12545.3
## - NE              1     14.23 17383 -12539.3
## - height          1     19.87 17388 -12530.3
## - avg_rbry_plyr   1     29.96 17398 -12514.4
## - avg_fuml_plyr   1    242.17 17611 -12181.2
## - avg_qbtdp_plyr  1   2422.08 19791  -8973.8
## 
## Step:  AIC=-12560.2
## ints ~ height + weight + forty1 + vertical1 + ARI + BAL + BUF + 
##     CAR + CLE + GB + HOU + JAC + MINN + NE + NYJ + OAK + PHI + 
##     SD + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## <none>                        17369 -12560.2
## - SD              1      1.37 17371 -12560.0
## - vertical1       1      1.42 17371 -12559.9
## - BAL             1      1.57 17371 -12559.7
## - BUF             1      1.79 17371 -12559.4
## - bad_weather_1   1      2.16 17372 -12558.8
## - WAS             1      2.43 17372 -12558.4
## - HOU             1      2.62 17372 -12558.1
## - OAK             1      2.81 17372 -12557.7
## - MINN            1      2.92 17372 -12557.6
## - PHI             1      2.99 17372 -12557.5
## - ARI             1      2.99 17372 -12557.5
## - NYJ             1      3.03 17373 -12557.4
## - avg_rbry_pos    1      3.26 17373 -12557.0
## - CAR             1      4.05 17374 -12555.8
## - CLE             1      4.71 17374 -12554.7
## - JAC             1      5.84 17375 -12553.0
## - GB              1      8.39 17378 -12548.9
## - avg_rectd_plyr  1      8.75 17378 -12548.4
## - weight          1      9.74 17379 -12546.8
## - forty1          1     10.42 17380 -12545.7
## - NE              1     13.78 17383 -12540.4
## - height          1     19.82 17389 -12530.8
## - avg_rbry_plyr   1     29.92 17399 -12514.9
## - avg_fuml_plyr   1    242.03 17612 -12181.9
## - avg_qbtdp_plyr  1   2422.00 19791  -8974.5

Pass Attempts

PreProcess:

set.seed(123)
splitpa <- sample.split(nfl_data$pa, SplitRatio = 0.7)
Trainpa <- subset(nfl_data, split == TRUE)
Testpa <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainpa, method = c("center", "scale"))
trainTransformedpa <- predict(preProcValues, Trainpa)
testTransformedpa <- predict(preProcValues, Testpa)

ggpairs:

ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("pa",colnames(filtered_nfl_data_fields[46:51]))])

paregform <- formula(paste("pa ~ ", 
                             paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegQBpa <- lm(paregform, data = trainTransformedpa)
summary(linRegQBpa)
## 
## Call:
## lm(formula = paregform, data = trainTransformedpa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1030 -0.0669 -0.0157  0.0397  4.5224 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      2.763e-15  2.304e-03   0.000 1.000000    
## height           5.881e-02  4.470e-03  13.158  < 2e-16 ***
## weight          -3.669e-02  4.189e-03  -8.758  < 2e-16 ***
## cold_weather    -1.546e-03  2.425e-03  -0.638 0.523669    
## hot_weather     -1.288e-03  2.325e-03  -0.554 0.579429    
## home_team_1     -3.172e-03  2.506e-03  -1.265 0.205762    
## forty1           2.154e-02  3.976e-03   5.418 6.07e-08 ***
## vertical1       -1.677e-02  3.057e-03  -5.486 4.15e-08 ***
## ARI              7.868e-04  3.222e-03   0.244 0.807111    
## ATL             -8.184e-03  3.238e-03  -2.528 0.011491 *  
## BAL             -1.113e-04  3.241e-03  -0.034 0.972591    
## BUF              8.983e-04  3.199e-03   0.281 0.778850    
## CAR             -1.715e-03  3.178e-03  -0.540 0.589378    
## CHI             -8.235e-03  3.143e-03  -2.620 0.008787 ** 
## CIN             -5.600e-03  3.201e-03  -1.750 0.080182 .  
## CLE              8.330e-03  3.186e-03   2.615 0.008932 ** 
## DAL             -1.518e-02  3.218e-03  -4.716 2.41e-06 ***
## DEN             -6.895e-03  3.230e-03  -2.134 0.032813 *  
## DET             -4.745e-03  3.186e-03  -1.489 0.136370    
## GB              -2.153e-02  3.280e-03  -6.563 5.37e-11 ***
## HOU              7.181e-03  3.241e-03   2.216 0.026717 *  
## IND             -4.968e-03  3.217e-03  -1.544 0.122511    
## JAC              3.626e-03  3.138e-03   1.156 0.247868    
## KC               3.694e-03  3.207e-03   1.152 0.249377    
## MIA             -1.993e-03  3.155e-03  -0.632 0.527592    
## MINN             4.361e-03  3.175e-03   1.374 0.169503    
## NE              -1.871e-02  3.316e-03  -5.644 1.68e-08 ***
## NOR             -1.518e-02  3.305e-03  -4.593 4.38e-06 ***
## NYG             -1.148e-02  3.231e-03  -3.554 0.000381 ***
## NYJ             -2.603e-03  3.219e-03  -0.809 0.418613    
## OAK             -2.043e-03  3.239e-03  -0.631 0.528265    
## PHI              3.831e-03  3.139e-03   1.221 0.222250    
## PIT             -7.229e-03  3.221e-03  -2.244 0.024827 *  
## SD              -1.680e-02  3.161e-03  -5.315 1.08e-07 ***
## SEA             -2.060e-03  3.281e-03  -0.628 0.530075    
## STL              3.392e-03  3.193e-03   1.062 0.288105    
## TB              -6.161e-03  3.163e-03  -1.948 0.051430 .  
## TEN             -5.033e-03  3.182e-03  -1.582 0.113715    
## WAS              2.904e-03  3.199e-03   0.908 0.364056    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -2.016e-02  2.942e-03  -6.854 7.34e-12 ***
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr   -3.353e-02  3.520e-03  -9.525  < 2e-16 ***
## avg_rbry_pos     1.909e-02  4.102e-03   4.654 3.26e-06 ***
## avg_fuml_plyr    1.015e-01  3.403e-03  29.822  < 2e-16 ***
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr   8.223e-01  3.696e-03 222.466  < 2e-16 ***
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -7.378e-04  2.650e-03  -0.278 0.780742    
## bad_weather_1   -4.319e-04  2.343e-03  -0.184 0.853791    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3819 on 27438 degrees of freedom
## Multiple R-squared:  0.8544, Adjusted R-squared:  0.8541 
## F-statistic:  3578 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegQBpa2 <- update(linRegQBpa, ~.-hot_weather-home_team_1-ATL-BAL-CLE-DAL-DEN-DET-KC
                      -NOR-OAK-SEA-STL-WAS-avg_trg_team-avg_tdr_team-avg_rbra_team
                      -avg_rbry_plyr-avg_fuml_team-avg_qbints_team-avg_qbtdp_team
                      -grass_1-bad_weather_1 )
summary(linRegQBpa2)
## 
## Call:
## lm(formula = pa ~ height + weight + cold_weather + forty1 + vertical1 + 
##     ARI + BUF + CAR + CHI + CIN + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NYG + NYJ + PHI + PIT + SD + TB + TEN + avg_rectd_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr, data = trainTransformedpa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1273 -0.0684 -0.0140  0.0358  4.5162 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.823e-15  2.311e-03   0.000  1.00000    
## height          5.863e-02  4.448e-03  13.180  < 2e-16 ***
## weight         -3.843e-02  4.181e-03  -9.192  < 2e-16 ***
## cold_weather    5.948e-04  2.362e-03   0.252  0.80116    
## forty1          2.767e-02  3.912e-03   7.074 1.54e-12 ***
## vertical1      -1.494e-02  3.046e-03  -4.907 9.30e-07 ***
## ARI             4.500e-03  2.365e-03   1.903  0.05706 .  
## BUF             3.347e-03  2.367e-03   1.414  0.15738    
## CAR             1.515e-04  2.363e-03   0.064  0.94888    
## CHI            -6.221e-03  2.367e-03  -2.628  0.00858 ** 
## CIN            -3.585e-03  2.366e-03  -1.516  0.12965    
## GB             -1.914e-02  2.388e-03  -8.012 1.17e-15 ***
## HOU             9.804e-03  2.372e-03   4.133 3.59e-05 ***
## IND            -1.935e-03  2.363e-03  -0.819  0.41288    
## JAC             5.974e-03  2.365e-03   2.526  0.01153 *  
## MIA             9.219e-04  2.360e-03   0.391  0.69600    
## MINN            5.977e-03  2.369e-03   2.523  0.01163 *  
## NE             -1.654e-02  2.416e-03  -6.849 7.60e-12 ***
## NYG            -8.542e-03  2.368e-03  -3.608  0.00031 ***
## NYJ            -6.759e-04  2.369e-03  -0.285  0.77535    
## PHI             5.807e-03  2.363e-03   2.458  0.01399 *  
## PIT            -4.942e-03  2.373e-03  -2.082  0.03731 *  
## SD             -1.396e-02  2.365e-03  -5.904 3.60e-09 ***
## TB             -3.594e-03  2.363e-03  -1.521  0.12829    
## TEN            -2.594e-03  2.364e-03  -1.097  0.27262    
## avg_rectd_plyr -2.529e-02  2.907e-03  -8.700  < 2e-16 ***
## avg_rbry_pos   -4.926e-03  3.434e-03  -1.434  0.15146    
## avg_fuml_plyr   9.268e-02  3.205e-03  28.919  < 2e-16 ***
## avg_qbtdp_plyr  8.233e-01  3.645e-03 225.904  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3832 on 27455 degrees of freedom
## Multiple R-squared:  0.8533, Adjusted R-squared:  0.8532 
## F-statistic:  5704 on 28 and 27455 DF,  p-value: < 2.2e-16
linRegQBpa3 <- update(linRegQBpa2, ~.-vertical1-IND-PHI-PIT )
summary(linRegQBpa3)
## 
## Call:
## lm(formula = pa ~ height + weight + cold_weather + forty1 + ARI + 
##     BUF + CAR + CHI + CIN + GB + HOU + JAC + MIA + MINN + NE + 
##     NYG + NYJ + SD + TB + TEN + avg_rectd_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr, data = trainTransformedpa)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1362 -0.0694 -0.0130  0.0356  4.5346 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.837e-15  2.313e-03   0.000 1.000000    
## height          5.816e-02  4.447e-03  13.079  < 2e-16 ***
## weight         -3.996e-02  4.171e-03  -9.580  < 2e-16 ***
## cold_weather    1.311e-04  2.351e-03   0.056 0.955524    
## forty1          3.773e-02  3.342e-03  11.290  < 2e-16 ***
## ARI             4.865e-03  2.351e-03   2.069 0.038516 *  
## BUF             3.949e-03  2.351e-03   1.680 0.093004 .  
## CAR             1.089e-04  2.349e-03   0.046 0.963033    
## CHI            -5.742e-03  2.352e-03  -2.441 0.014637 *  
## CIN            -3.356e-03  2.351e-03  -1.427 0.153498    
## GB             -1.861e-02  2.370e-03  -7.849 4.34e-15 ***
## HOU             9.521e-03  2.359e-03   4.037 5.44e-05 ***
## JAC             5.286e-03  2.348e-03   2.251 0.024380 *  
## MIA             1.332e-03  2.346e-03   0.568 0.570156    
## MINN            5.619e-03  2.355e-03   2.386 0.017022 *  
## NE             -1.624e-02  2.400e-03  -6.768 1.33e-11 ***
## NYG            -8.348e-03  2.353e-03  -3.548 0.000389 ***
## NYJ            -1.280e-03  2.350e-03  -0.544 0.586103    
## SD             -1.374e-02  2.353e-03  -5.841 5.25e-09 ***
## TB             -3.308e-03  2.350e-03  -1.408 0.159203    
## TEN            -2.767e-03  2.350e-03  -1.177 0.239039    
## avg_rectd_plyr -2.617e-02  2.904e-03  -9.010  < 2e-16 ***
## avg_rbry_pos   -4.051e-03  3.427e-03  -1.182 0.237211    
## avg_fuml_plyr   9.350e-02  3.199e-03  29.232  < 2e-16 ***
## avg_qbtdp_plyr  8.231e-01  3.643e-03 225.966  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3834 on 27459 degrees of freedom
## Multiple R-squared:  0.8531, Adjusted R-squared:  0.853 
## F-statistic:  6645 on 24 and 27459 DF,  p-value: < 2.2e-16

R2 is strong. This stat is the catalyst Ints, completions, TD’s. You have to attempt a pass in order to achieve a stat in any of these three categories.

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

PaPredicted <- predict(linRegQBpa3, newdata = testTransformedpa)

SSEpa <- sum((PaPredicted - testTransformedpa$pa)^2)
SSTpa <- sum((mean(nfl_data$pa)-testTransformedpa$pa)^2)
r2_pa <- 1 - SSEpa/SSTpa 
r2_pa
## [1] 0.9870137
rmse_pa <- sqrt(SSEpa/nrow(testTransformedpa))
rmse_pa
## [1] 0.3953472

Regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegQBpa3, which = c(1:3,5))

Very similar patterns to completions and yards. Some strong tails, so the data may not be normally distributed

Summary statistics:

confint(linRegQBpa3)
##                        2.5 %       97.5 %
## (Intercept)    -0.0045332724  0.004533272
## height          0.0494453252  0.066877140
## weight         -0.0481324757 -0.031781419
## cold_weather   -0.0044762676  0.004738466
## forty1          0.0311803541  0.044281015
## ARI             0.0002571222  0.009472993
## BUF            -0.0006588596  0.008557851
## CAR            -0.0044955296  0.004713284
## CHI            -0.0103515944 -0.001132075
## CIN            -0.0079650992  0.001252658
## GB             -0.0232514031 -0.013959285
## HOU             0.0048978676  0.014143962
## JAC             0.0006836263  0.009887708
## MIA            -0.0032657529  0.005929682
## MINN            0.0010038754  0.010234782
## NE             -0.0209465699 -0.011538645
## NYG            -0.0129596970 -0.003735903
## NYJ            -0.0058856085  0.003326504
## SD             -0.0183540586 -0.009130940
## TB             -0.0079143787  0.001297788
## TEN            -0.0073740699  0.001839441
## avg_rectd_plyr -0.0318627125 -0.020476836
## avg_rbry_pos   -0.0107684004  0.002666476
## avg_fuml_plyr   0.0872311724  0.099770017
## avg_qbtdp_plyr  0.8159438330  0.830222848
coef(summary(linRegQBpa3))
##                     Estimate  Std. Error       t value      Pr(>|t|)
## (Intercept)     2.837106e-15 0.002312835  1.226679e-12  1.000000e+00
## height          5.816123e-02 0.004446777  1.307941e+01  5.647188e-39
## weight         -3.995695e-02 0.004171081 -9.579519e+00  1.054241e-21
## cold_weather    1.310994e-04 0.002350637  5.577188e-02  9.555239e-01
## forty1          3.773068e-02 0.003341919  1.129012e+01  1.705538e-29
## ARI             4.865058e-03 0.002350927  2.069421e+00  3.851593e-02
## BUF             3.949496e-03 0.002351141  1.679821e+00  9.300359e-02
## CAR             1.088773e-04 0.002349127  4.634798e-02  9.630332e-01
## CHI            -5.741835e-03 0.002351858 -2.441404e+00  1.463656e-02
## CIN            -3.356220e-03 0.002351408 -1.427324e+00  1.534980e-01
## GB             -1.860534e-02 0.002370377 -7.849106e+00  4.342062e-15
## HOU             9.520915e-03 0.002358637  4.036617e+00  5.437438e-05
## JAC             5.285667e-03 0.002347920  2.251213e+00  2.437993e-02
## MIA             1.331964e-03 0.002345714  5.678290e-01  5.701557e-01
## MINN            5.619329e-03 0.002354763  2.386367e+00  1.702247e-02
## NE             -1.624261e-02 0.002399919 -6.767981e+00  1.332176e-11
## NYG            -8.347800e-03 0.002352948 -3.547804e+00  3.891041e-04
## NYJ            -1.279552e-03 0.002349968 -5.444977e-01  5.861035e-01
## SD             -1.374250e-02 0.002352776 -5.840972e+00  5.248161e-09
## TB             -3.308296e-03 0.002349982 -1.407796e+00  1.592028e-01
## TEN            -2.767315e-03 0.002350325 -1.177418e+00  2.390390e-01
## avg_rectd_plyr -2.616977e-02 0.002904486 -9.010123e+00  2.188484e-19
## avg_rbry_pos   -4.050962e-03 0.003427176 -1.182012e+00  2.372113e-01
## avg_fuml_plyr   9.350059e-02 0.003198603  2.923170e+01 5.249398e-185
## avg_qbtdp_plyr  8.230833e-01 0.003642512  2.259658e+02  0.000000e+00
anova(linRegQBpa3)
## Analysis of Variance Table
## 
## Response: pa
##                   Df Sum Sq Mean Sq    F value    Pr(>F)    
## height             1 1950.3  1950.3 13265.6253 < 2.2e-16 ***
## weight             1  461.7   461.7  3140.2425 < 2.2e-16 ***
## cold_weather       1    0.0     0.0     0.0000  0.995281    
## forty1             1 5580.4  5580.4 37957.4316 < 2.2e-16 ***
## ARI                1    1.3     1.3     8.6924  0.003198 ** 
## BUF                1    1.2     1.2     8.3499  0.003860 ** 
## CAR                1    9.9     9.9    67.1807 2.584e-16 ***
## CHI                1    0.3     0.3     2.2304  0.135331    
## CIN                1    3.0     3.0    20.5662 5.785e-06 ***
## GB                 1    0.2     0.2     1.2281  0.267782    
## HOU                1   12.2    12.2    83.0773 < 2.2e-16 ***
## JAC                1    0.8     0.8     5.1288  0.023540 *  
## MIA                1    0.4     0.4     2.5248  0.112079    
## MINN               1    0.8     0.8     5.7576  0.016424 *  
## NE                 1   43.7    43.7   297.5004 < 2.2e-16 ***
## NYG                1    8.5     8.5    57.8649 2.897e-14 ***
## NYJ                1    0.2     0.2     1.6841  0.194393    
## SD                 1   19.9    19.9   135.1058 < 2.2e-16 ***
## TB                 1    2.5     2.5    17.3398 3.135e-05 ***
## TEN                1    5.8     5.8    39.2418 3.800e-10 ***
## avg_rectd_plyr     1 1877.2  1877.2 12768.2759 < 2.2e-16 ***
## avg_rbry_pos       1  341.1   341.1  2320.1948 < 2.2e-16 ***
## avg_fuml_plyr      1 5617.8  5617.8 38212.0971 < 2.2e-16 ***
## avg_qbtdp_plyr     1 7506.8  7506.8 51060.5597 < 2.2e-16 ***
## Residuals      27459 4037.0     0.1                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_pa <- step(lm(paregform, data = trainTransformedpa), direction = "backward")
## Start:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-52865.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BAL             1       0.0  4001.9 -52867
## - bad_weather_1   1       0.0  4001.9 -52867
## - ARI             1       0.0  4001.9 -52867
## - grass_1         1       0.0  4001.9 -52867
## - BUF             1       0.0  4001.9 -52867
## - CAR             1       0.0  4001.9 -52867
## - hot_weather     1       0.0  4001.9 -52867
## - SEA             1       0.1  4001.9 -52867
## - OAK             1       0.1  4001.9 -52867
## - MIA             1       0.1  4001.9 -52867
## - cold_weather    1       0.1  4001.9 -52867
## - NYJ             1       0.1  4002.0 -52867
## - WAS             1       0.1  4002.0 -52866
## - STL             1       0.2  4002.1 -52866
## - KC              1       0.2  4002.1 -52866
## - JAC             1       0.2  4002.1 -52866
## - PHI             1       0.2  4002.1 -52866
## - home_team_1     1       0.2  4002.1 -52866
## - MINN            1       0.3  4002.2 -52865
## <none>                         4001.9 -52865
## - DET             1       0.3  4002.2 -52865
## - IND             1       0.3  4002.2 -52865
## - TEN             1       0.4  4002.3 -52865
## - CIN             1       0.4  4002.3 -52864
## - TB              1       0.6  4002.4 -52863
## - DEN             1       0.7  4002.6 -52863
## - HOU             1       0.7  4002.6 -52862
## - PIT             1       0.7  4002.6 -52862
## - ATL             1       0.9  4002.8 -52861
## - CLE             1       1.0  4002.9 -52860
## - CHI             1       1.0  4002.9 -52860
## - NYG             1       1.8  4003.7 -52855
## - NOR             1       3.1  4005.0 -52846
## - avg_rbry_pos    1       3.2  4005.0 -52846
## - DAL             1       3.2  4005.1 -52845
## - SD              1       4.1  4006.0 -52839
## - forty1          1       4.3  4006.2 -52838
## - vertical1       1       4.4  4006.3 -52837
## - NE              1       4.6  4006.5 -52835
## - GB              1       6.3  4008.2 -52824
## - avg_rectd_plyr  1       6.9  4008.7 -52820
## - weight          1      11.2  4013.1 -52790
## - avg_rbry_plyr   1      13.2  4015.1 -52776
## - height          1      25.3  4027.1 -52694
## - avg_fuml_plyr   1     129.7  4131.6 -51991
## - avg_qbtdp_plyr  1    7218.4 11220.2 -24532
## 
## Step:  AIC=-52867.22
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - bad_weather_1   1       0.0  4001.9 -52869
## - grass_1         1       0.0  4001.9 -52869
## - ARI             1       0.0  4001.9 -52869
## - BUF             1       0.0  4001.9 -52869
## - hot_weather     1       0.0  4001.9 -52869
## - CAR             1       0.1  4001.9 -52869
## - cold_weather    1       0.1  4001.9 -52869
## - MIA             1       0.1  4002.0 -52869
## - OAK             1       0.1  4002.0 -52869
## - SEA             1       0.1  4002.0 -52869
## - NYJ             1       0.1  4002.0 -52868
## - WAS             1       0.2  4002.1 -52868
## - STL             1       0.2  4002.1 -52868
## - home_team_1     1       0.2  4002.1 -52868
## - JAC             1       0.3  4002.1 -52867
## - KC              1       0.3  4002.2 -52867
## <none>                         4001.9 -52867
## - PHI             1       0.3  4002.2 -52867
## - MINN            1       0.4  4002.3 -52867
## - DET             1       0.4  4002.3 -52866
## - IND             1       0.5  4002.3 -52866
## - TEN             1       0.5  4002.4 -52866
## - CIN             1       0.6  4002.5 -52865
## - TB              1       0.7  4002.6 -52864
## - DEN             1       0.9  4002.8 -52863
## - PIT             1       1.0  4002.9 -52863
## - HOU             1       1.0  4002.9 -52863
## - ATL             1       1.2  4003.1 -52861
## - CHI             1       1.3  4003.2 -52860
## - CLE             1       1.3  4003.2 -52860
## - NYG             1       2.5  4004.3 -52852
## - avg_rbry_pos    1       3.2  4005.0 -52848
## - NOR             1       4.1  4006.0 -52841
## - DAL             1       4.3  4006.2 -52840
## - forty1          1       4.3  4006.2 -52840
## - vertical1       1       4.4  4006.3 -52839
## - SD              1       5.4  4007.2 -52832
## - NE              1       6.2  4008.1 -52826
## - avg_rectd_plyr  1       6.9  4008.7 -52822
## - GB              1       8.4  4010.3 -52811
## - weight          1      11.2  4013.1 -52792
## - avg_rbry_plyr   1      13.2  4015.1 -52778
## - height          1      25.3  4027.1 -52696
## - avg_fuml_plyr   1     129.7  4131.6 -51992
## - avg_qbtdp_plyr  1    7218.4 11220.3 -24534
## 
## Step:  AIC=-52869.19
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq     RSS    AIC
## - grass_1         1       0.0  4001.9 -52871
## - ARI             1       0.0  4001.9 -52871
## - BUF             1       0.0  4001.9 -52871
## - hot_weather     1       0.0  4001.9 -52871
## - CAR             1       0.1  4001.9 -52871
## - cold_weather    1       0.1  4002.0 -52871
## - MIA             1       0.1  4002.0 -52871
## - OAK             1       0.1  4002.0 -52871
## - SEA             1       0.1  4002.0 -52871
## - NYJ             1       0.1  4002.0 -52870
## - WAS             1       0.2  4002.1 -52870
## - STL             1       0.2  4002.1 -52870
## - home_team_1     1       0.2  4002.1 -52870
## - JAC             1       0.3  4002.2 -52869
## - KC              1       0.3  4002.2 -52869
## <none>                         4001.9 -52869
## - PHI             1       0.3  4002.2 -52869
## - MINN            1       0.4  4002.3 -52869
## - DET             1       0.4  4002.3 -52868
## - IND             1       0.5  4002.3 -52868
## - TEN             1       0.5  4002.4 -52868
## - CIN             1       0.6  4002.5 -52867
## - TB              1       0.7  4002.6 -52866
## - DEN             1       0.9  4002.8 -52865
## - HOU             1       1.0  4002.9 -52865
## - PIT             1       1.0  4002.9 -52865
## - ATL             1       1.2  4003.1 -52863
## - CHI             1       1.3  4003.2 -52862
## - CLE             1       1.3  4003.2 -52862
## - NYG             1       2.5  4004.4 -52854
## - avg_rbry_pos    1       3.2  4005.0 -52850
## - NOR             1       4.1  4006.0 -52843
## - DAL             1       4.3  4006.2 -52842
## - forty1          1       4.3  4006.2 -52842
## - vertical1       1       4.4  4006.3 -52841
## - SD              1       5.4  4007.2 -52834
## - NE              1       6.2  4008.1 -52828
## - avg_rectd_plyr  1       6.8  4008.7 -52824
## - GB              1       8.4  4010.3 -52813
## - weight          1      11.2  4013.1 -52794
## - avg_rbry_plyr   1      13.2  4015.1 -52780
## - height          1      25.3  4027.1 -52698
## - avg_fuml_plyr   1     129.7  4131.6 -51994
## - avg_qbtdp_plyr  1    7218.4 11220.3 -24536
## 
## Step:  AIC=-52871.11
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BUF + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - ARI             1       0.0  4001.9 -52873
## - BUF             1       0.0  4001.9 -52873
## - hot_weather     1       0.0  4002.0 -52873
## - CAR             1       0.1  4002.0 -52873
## - cold_weather    1       0.1  4002.0 -52873
## - SEA             1       0.1  4002.0 -52873
## - MIA             1       0.1  4002.0 -52873
## - OAK             1       0.1  4002.0 -52873
## - NYJ             1       0.1  4002.0 -52872
## - WAS             1       0.2  4002.1 -52872
## - STL             1       0.2  4002.1 -52872
## - KC              1       0.3  4002.2 -52871
## - home_team_1     1       0.3  4002.2 -52871
## - JAC             1       0.3  4002.2 -52871
## - PHI             1       0.3  4002.2 -52871
## <none>                         4001.9 -52871
## - MINN            1       0.4  4002.3 -52870
## - DET             1       0.4  4002.3 -52870
## - IND             1       0.4  4002.3 -52870
## - TEN             1       0.5  4002.4 -52870
## - CIN             1       0.6  4002.5 -52869
## - TB              1       0.7  4002.6 -52868
## - DEN             1       0.9  4002.8 -52867
## - HOU             1       1.0  4002.9 -52866
## - PIT             1       1.0  4002.9 -52866
## - ATL             1       1.2  4003.1 -52865
## - CLE             1       1.3  4003.2 -52864
## - CHI             1       1.3  4003.2 -52864
## - NYG             1       2.5  4004.4 -52856
## - avg_rbry_pos    1       3.2  4005.1 -52851
## - NOR             1       4.1  4006.0 -52845
## - DAL             1       4.3  4006.2 -52844
## - forty1          1       4.3  4006.2 -52844
## - vertical1       1       4.4  4006.3 -52843
## - SD              1       5.4  4007.3 -52836
## - NE              1       6.3  4008.2 -52830
## - avg_rectd_plyr  1       6.9  4008.8 -52826
## - GB              1       8.5  4010.4 -52815
## - weight          1      11.2  4013.1 -52796
## - avg_rbry_plyr   1      13.2  4015.1 -52782
## - height          1      25.3  4027.2 -52700
## - avg_fuml_plyr   1     129.7  4131.6 -51996
## - avg_qbtdp_plyr  1    7218.8 11220.7 -24537
## 
## Step:  AIC=-52873.01
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - BUF             1       0.0  4001.9 -52875
## - hot_weather     1       0.0  4002.0 -52875
## - cold_weather    1       0.1  4002.0 -52875
## - CAR             1       0.1  4002.0 -52874
## - SEA             1       0.1  4002.0 -52874
## - MIA             1       0.1  4002.0 -52874
## - OAK             1       0.1  4002.0 -52874
## - WAS             1       0.1  4002.1 -52874
## - NYJ             1       0.2  4002.1 -52874
## - STL             1       0.2  4002.1 -52874
## - KC              1       0.2  4002.2 -52873
## - JAC             1       0.2  4002.2 -52873
## - PHI             1       0.3  4002.2 -52873
## - home_team_1     1       0.3  4002.2 -52873
## <none>                         4001.9 -52873
## - MINN            1       0.4  4002.3 -52872
## - DET             1       0.5  4002.4 -52871
## - IND             1       0.6  4002.5 -52871
## - TEN             1       0.6  4002.5 -52871
## - CIN             1       0.7  4002.6 -52870
## - TB              1       0.9  4002.8 -52869
## - HOU             1       1.0  4002.9 -52868
## - DEN             1       1.1  4003.0 -52868
## - PIT             1       1.2  4003.1 -52867
## - CLE             1       1.4  4003.3 -52866
## - ATL             1       1.5  4003.4 -52865
## - CHI             1       1.6  4003.5 -52864
## - NYG             1       2.9  4004.8 -52855
## - avg_rbry_pos    1       3.2  4005.1 -52853
## - forty1          1       4.3  4006.2 -52846
## - vertical1       1       4.4  4006.3 -52845
## - NOR             1       4.9  4006.8 -52842
## - DAL             1       5.0  4006.9 -52841
## - SD              1       6.2  4008.2 -52832
## - avg_rectd_plyr  1       6.9  4008.8 -52828
## - NE              1       7.1  4009.1 -52826
## - GB              1       9.8  4011.7 -52808
## - weight          1      11.2  4013.1 -52798
## - avg_rbry_plyr   1      13.3  4015.2 -52784
## - height          1      25.4  4027.3 -52701
## - avg_fuml_plyr   1     129.9  4131.8 -51997
## - avg_qbtdp_plyr  1    7223.1 11225.0 -24529
## 
## Step:  AIC=-52874.93
## pa ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + CAR + CHI + CIN + CLE + DAL + 
##     DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - hot_weather     1       0.0  4002.0 -52877
## - cold_weather    1       0.1  4002.0 -52876
## - CAR             1       0.1  4002.0 -52876
## - SEA             1       0.1  4002.1 -52876
## - WAS             1       0.1  4002.1 -52876
## - MIA             1       0.1  4002.1 -52876
## - OAK             1       0.1  4002.1 -52876
## - NYJ             1       0.2  4002.1 -52876
## - STL             1       0.2  4002.1 -52875
## - KC              1       0.2  4002.2 -52875
## - JAC             1       0.2  4002.2 -52875
## - PHI             1       0.3  4002.2 -52875
## - home_team_1     1       0.3  4002.2 -52875
## <none>                         4001.9 -52875
## - MINN            1       0.4  4002.3 -52874
## - DET             1       0.6  4002.5 -52873
## - IND             1       0.6  4002.6 -52873
## - TEN             1       0.7  4002.6 -52872
## - CIN             1       0.8  4002.7 -52871
## - TB              1       1.0  4002.9 -52870
## - HOU             1       1.0  4003.0 -52870
## - DEN             1       1.2  4003.1 -52869
## - PIT             1       1.3  4003.3 -52868
## - CLE             1       1.4  4003.3 -52867
## - ATL             1       1.6  4003.5 -52866
## - CHI             1       1.7  4003.7 -52865
## - NYG             1       3.2  4005.1 -52855
## - avg_rbry_pos    1       3.2  4005.1 -52855
## - forty1          1       4.3  4006.2 -52848
## - vertical1       1       4.4  4006.4 -52847
## - NOR             1       5.3  4007.2 -52841
## - DAL             1       5.4  4007.3 -52840
## - SD              1       6.8  4008.7 -52831
## - avg_rectd_plyr  1       6.9  4008.8 -52830
## - NE              1       7.7  4009.7 -52824
## - GB              1      10.6  4012.5 -52804
## - weight          1      11.3  4013.2 -52800
## - avg_rbry_plyr   1      13.3  4015.2 -52786
## - height          1      25.4  4027.4 -52703
## - avg_fuml_plyr   1     130.0  4131.9 -51998
## - avg_qbtdp_plyr  1    7226.4 11228.4 -24523
## 
## Step:  AIC=-52876.61
## pa ~ height + weight + cold_weather + home_team_1 + forty1 + 
##     vertical1 + ATL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     GB + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - cold_weather    1       0.1  4002.0 -52878
## - CAR             1       0.1  4002.1 -52878
## - MIA             1       0.1  4002.1 -52878
## - SEA             1       0.1  4002.1 -52878
## - WAS             1       0.1  4002.1 -52878
## - OAK             1       0.1  4002.1 -52878
## - NYJ             1       0.2  4002.2 -52877
## - STL             1       0.2  4002.2 -52877
## - KC              1       0.2  4002.2 -52877
## - JAC             1       0.2  4002.2 -52877
## - PHI             1       0.3  4002.2 -52877
## - home_team_1     1       0.3  4002.3 -52877
## <none>                         4002.0 -52877
## - MINN            1       0.4  4002.3 -52876
## - DET             1       0.6  4002.6 -52875
## - IND             1       0.6  4002.6 -52874
## - TEN             1       0.7  4002.7 -52874
## - CIN             1       0.8  4002.8 -52873
## - TB              1       1.0  4003.0 -52872
## - HOU             1       1.0  4003.0 -52872
## - DEN             1       1.2  4003.2 -52870
## - PIT             1       1.3  4003.3 -52869
## - CLE             1       1.4  4003.4 -52869
## - ATL             1       1.6  4003.6 -52868
## - CHI             1       1.7  4003.7 -52867
## - NYG             1       3.1  4005.1 -52857
## - avg_rbry_pos    1       3.2  4005.2 -52857
## - forty1          1       4.3  4006.2 -52849
## - vertical1       1       4.4  4006.4 -52848
## - NOR             1       5.3  4007.3 -52842
## - DAL             1       5.4  4007.4 -52842
## - SD              1       6.8  4008.8 -52832
## - avg_rectd_plyr  1       6.9  4008.8 -52831
## - NE              1       7.7  4009.7 -52825
## - GB              1      10.6  4012.6 -52806
## - weight          1      11.2  4013.2 -52801
## - avg_rbry_plyr   1      13.3  4015.3 -52787
## - height          1      25.4  4027.4 -52705
## - avg_fuml_plyr   1     130.0  4132.0 -52000
## - avg_qbtdp_plyr  1    7226.8 11228.8 -24524
## 
## Step:  AIC=-52878.17
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL + 
##     CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + 
##     JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + 
##     PIT + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - CAR             1       0.1  4002.1 -52879
## - MIA             1       0.1  4002.2 -52879
## - OAK             1       0.1  4002.2 -52879
## - WAS             1       0.1  4002.2 -52879
## - SEA             1       0.1  4002.2 -52879
## - NYJ             1       0.2  4002.2 -52879
## - STL             1       0.2  4002.2 -52879
## - KC              1       0.2  4002.3 -52879
## - JAC             1       0.2  4002.3 -52878
## - PHI             1       0.3  4002.3 -52878
## <none>                         4002.0 -52878
## - home_team_1     1       0.3  4002.3 -52878
## - MINN            1       0.4  4002.4 -52878
## - DET             1       0.6  4002.6 -52876
## - IND             1       0.6  4002.7 -52876
## - TEN             1       0.7  4002.7 -52876
## - CIN             1       0.8  4002.9 -52875
## - TB              1       1.0  4003.0 -52873
## - HOU             1       1.1  4003.1 -52873
## - DEN             1       1.2  4003.3 -52872
## - CLE             1       1.4  4003.4 -52871
## - PIT             1       1.4  4003.4 -52871
## - ATL             1       1.6  4003.6 -52869
## - CHI             1       1.7  4003.8 -52868
## - avg_rbry_pos    1       3.2  4005.2 -52858
## - NYG             1       3.2  4005.2 -52858
## - forty1          1       4.3  4006.3 -52851
## - vertical1       1       4.4  4006.5 -52850
## - NOR             1       5.3  4007.3 -52844
## - DAL             1       5.4  4007.4 -52843
## - SD              1       6.8  4008.8 -52834
## - avg_rectd_plyr  1       6.9  4008.9 -52833
## - NE              1       7.9  4009.9 -52826
## - GB              1      10.7  4012.8 -52806
## - weight          1      11.3  4013.3 -52803
## - avg_rbry_plyr   1      13.3  4015.3 -52789
## - height          1      25.5  4027.5 -52706
## - avg_fuml_plyr   1     130.1  4132.1 -52001
## - avg_qbtdp_plyr  1    7226.8 11228.8 -24525
## 
## Step:  AIC=-52879.46
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + 
##     SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - MIA             1       0.1  4002.2 -52881
## - OAK             1       0.1  4002.2 -52881
## - SEA             1       0.1  4002.2 -52881
## - NYJ             1       0.2  4002.3 -52880
## - WAS             1       0.2  4002.3 -52880
## - STL             1       0.3  4002.4 -52880
## <none>                         4002.1 -52879
## - KC              1       0.3  4002.4 -52879
## - home_team_1     1       0.3  4002.5 -52879
## - JAC             1       0.3  4002.5 -52879
## - PHI             1       0.3  4002.5 -52879
## - MINN            1       0.5  4002.6 -52878
## - DET             1       0.5  4002.6 -52878
## - IND             1       0.6  4002.7 -52878
## - TEN             1       0.6  4002.7 -52877
## - CIN             1       0.7  4002.9 -52876
## - TB              1       0.9  4003.0 -52875
## - DEN             1       1.1  4003.3 -52874
## - HOU             1       1.2  4003.4 -52873
## - PIT             1       1.3  4003.4 -52873
## - ATL             1       1.5  4003.6 -52871
## - CLE             1       1.6  4003.7 -52871
## - CHI             1       1.6  4003.8 -52870
## - NYG             1       3.1  4005.2 -52860
## - avg_rbry_pos    1       3.2  4005.4 -52859
## - forty1          1       4.3  4006.4 -52852
## - vertical1       1       4.5  4006.6 -52851
## - NOR             1       5.2  4007.3 -52846
## - DAL             1       5.3  4007.4 -52845
## - SD              1       6.7  4008.9 -52835
## - avg_rectd_plyr  1       6.8  4009.0 -52834
## - NE              1       7.8  4009.9 -52828
## - GB              1      10.8  4012.9 -52808
## - weight          1      11.4  4013.5 -52804
## - avg_rbry_plyr   1      13.4  4015.5 -52790
## - height          1      25.6  4027.7 -52706
## - avg_fuml_plyr   1     130.1  4132.2 -52002
## - avg_qbtdp_plyr  1    7228.0 11230.2 -24524
## 
## Step:  AIC=-52880.83
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - OAK             1       0.1  4002.3 -52882
## - SEA             1       0.1  4002.3 -52882
## - NYJ             1       0.1  4002.4 -52882
## - WAS             1       0.2  4002.5 -52881
## <none>                         4002.2 -52881
## - home_team_1     1       0.3  4002.6 -52881
## - STL             1       0.3  4002.6 -52881
## - KC              1       0.4  4002.6 -52880
## - JAC             1       0.4  4002.6 -52880
## - PHI             1       0.4  4002.6 -52880
## - DET             1       0.4  4002.7 -52880
## - IND             1       0.5  4002.7 -52879
## - TEN             1       0.5  4002.8 -52879
## - MINN            1       0.5  4002.8 -52879
## - CIN             1       0.7  4002.9 -52878
## - TB              1       0.8  4003.1 -52877
## - DEN             1       1.1  4003.3 -52876
## - PIT             1       1.2  4003.5 -52874
## - HOU             1       1.4  4003.6 -52873
## - ATL             1       1.4  4003.6 -52873
## - CHI             1       1.6  4003.8 -52872
## - CLE             1       1.7  4004.0 -52871
## - NYG             1       3.0  4005.2 -52862
## - avg_rbry_pos    1       3.2  4005.4 -52861
## - forty1          1       4.2  4006.5 -52854
## - vertical1       1       4.4  4006.7 -52852
## - NOR             1       5.1  4007.3 -52848
## - DAL             1       5.2  4007.4 -52847
## - SD              1       6.6  4008.9 -52837
## - avg_rectd_plyr  1       6.9  4009.1 -52836
## - NE              1       7.7  4010.0 -52830
## - GB              1      10.7  4013.0 -52809
## - weight          1      11.3  4013.6 -52805
## - avg_rbry_plyr   1      13.3  4015.6 -52791
## - height          1      25.6  4027.8 -52708
## - avg_fuml_plyr   1     130.0  4132.2 -52004
## - avg_qbtdp_plyr  1    7230.4 11232.6 -24520
## 
## Step:  AIC=-52882.36
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - SEA             1       0.1  4002.4 -52884
## - NYJ             1       0.1  4002.4 -52884
## - WAS             1       0.3  4002.6 -52882
## <none>                         4002.3 -52882
## - home_team_1     1       0.3  4002.6 -52882
## - STL             1       0.4  4002.7 -52882
## - DET             1       0.4  4002.7 -52882
## - KC              1       0.4  4002.7 -52881
## - JAC             1       0.4  4002.8 -52881
## - IND             1       0.5  4002.8 -52881
## - PHI             1       0.5  4002.8 -52881
## - TEN             1       0.5  4002.8 -52881
## - MINN            1       0.6  4002.9 -52880
## - CIN             1       0.6  4002.9 -52880
## - TB              1       0.8  4003.1 -52879
## - DEN             1       1.0  4003.3 -52877
## - PIT             1       1.2  4003.5 -52876
## - ATL             1       1.3  4003.6 -52875
## - HOU             1       1.5  4003.8 -52874
## - CHI             1       1.5  4003.8 -52874
## - CLE             1       1.9  4004.2 -52871
## - NYG             1       2.9  4005.2 -52864
## - avg_rbry_pos    1       3.2  4005.5 -52863
## - forty1          1       4.3  4006.6 -52855
## - vertical1       1       4.4  4006.7 -52854
## - NOR             1       5.0  4007.3 -52850
## - DAL             1       5.1  4007.4 -52849
## - SD              1       6.6  4008.9 -52839
## - avg_rectd_plyr  1       6.9  4009.2 -52837
## - NE              1       7.7  4010.0 -52832
## - GB              1      10.7  4013.0 -52811
## - weight          1      11.3  4013.6 -52807
## - avg_rbry_plyr   1      13.3  4015.6 -52793
## - height          1      25.5  4027.8 -52710
## - avg_fuml_plyr   1     130.2  4132.5 -52005
## - avg_qbtdp_plyr  1    7230.3 11232.6 -24522
## 
## Step:  AIC=-52883.97
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## - NYJ             1       0.1  4002.4 -52885
## <none>                         4002.4 -52884
## - WAS             1       0.3  4002.7 -52884
## - home_team_1     1       0.3  4002.7 -52884
## - DET             1       0.4  4002.7 -52883
## - IND             1       0.4  4002.8 -52883
## - STL             1       0.4  4002.8 -52883
## - TEN             1       0.5  4002.8 -52883
## - KC              1       0.5  4002.8 -52883
## - JAC             1       0.5  4002.9 -52883
## - PHI             1       0.5  4002.9 -52882
## - CIN             1       0.6  4002.9 -52882
## - MINN            1       0.7  4003.0 -52881
## - TB              1       0.7  4003.1 -52881
## - DEN             1       1.0  4003.3 -52879
## - PIT             1       1.1  4003.5 -52878
## - ATL             1       1.3  4003.6 -52877
## - CHI             1       1.5  4003.8 -52876
## - HOU             1       1.6  4004.0 -52875
## - CLE             1       2.0  4004.4 -52872
## - NYG             1       2.9  4005.2 -52866
## - avg_rbry_pos    1       3.2  4005.6 -52864
## - forty1          1       4.3  4006.6 -52857
## - vertical1       1       4.4  4006.8 -52855
## - NOR             1       5.0  4007.3 -52852
## - DAL             1       5.1  4007.4 -52851
## - SD              1       6.5  4008.9 -52841
## - avg_rectd_plyr  1       6.9  4009.2 -52839
## - NE              1       7.7  4010.0 -52833
## - GB              1      10.7  4013.1 -52812
## - weight          1      11.3  4013.7 -52808
## - avg_rbry_plyr   1      13.4  4015.7 -52794
## - height          1      25.7  4028.1 -52710
## - avg_fuml_plyr   1     130.7  4133.0 -52003
## - avg_qbtdp_plyr  1    7246.9 11249.3 -24483
## 
## Step:  AIC=-52885.4
## pa ~ height + weight + home_team_1 + forty1 + vertical1 + ATL + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     KC + MINN + NE + NOR + NYG + PHI + PIT + SD + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr
## 
##                  Df Sum of Sq     RSS    AIC
## <none>                         4002.4 -52885
## - DET             1       0.3  4002.8 -52885
## - home_team_1     1       0.3  4002.8 -52885
## - WAS             1       0.4  4002.8 -52885
## - IND             1       0.4  4002.8 -52885
## - TEN             1       0.4  4002.9 -52885
## - STL             1       0.5  4002.9 -52884
## - KC              1       0.5  4003.0 -52884
## - CIN             1       0.5  4003.0 -52884
## - JAC             1       0.6  4003.0 -52884
## - PHI             1       0.6  4003.0 -52883
## - TB              1       0.7  4003.1 -52883
## - MINN            1       0.7  4003.2 -52882
## - DEN             1       0.9  4003.4 -52881
## - PIT             1       1.1  4003.5 -52880
## - ATL             1       1.2  4003.7 -52879
## - CHI             1       1.4  4003.8 -52878
## - HOU             1       1.7  4004.1 -52876
## - CLE             1       2.1  4004.6 -52873
## - NYG             1       2.8  4005.2 -52868
## - avg_rbry_pos    1       3.2  4005.7 -52865
## - forty1          1       4.2  4006.7 -52858
## - vertical1       1       4.6  4007.0 -52856
## - NOR             1       4.9  4007.4 -52854
## - DAL             1       5.0  4007.4 -52853
## - SD              1       6.4  4008.9 -52843
## - avg_rectd_plyr  1       6.9  4009.3 -52840
## - NE              1       7.6  4010.0 -52835
## - GB              1      10.6  4013.1 -52814
## - weight          1      11.3  4013.7 -52810
## - avg_rbry_plyr   1      13.4  4015.9 -52795
## - height          1      25.7  4028.2 -52711
## - avg_fuml_plyr   1     130.6  4133.1 -52005
## - avg_qbtdp_plyr  1    7256.2 11258.6 -24463

Rushing Stats

Rushing Yards

PreProcess:

set.seed(123)
splitry <- sample.split(nfl_data$ry, SplitRatio = 0.7)
Trainry <- subset(nfl_data, split == TRUE)
Testry <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainry, method = c("center", "scale"))
trainTransformedry <- predict(preProcValues, Trainry)
testTransformedry <- predict(preProcValues, Testry)

ggpairs:

ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("ry",colnames(filtered_nfl_data_fields[46:51]))])

ryregform <- formula(paste("ry ~ ", 
                           paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegRushYd <- lm(ryregform, data = trainTransformedry)
summary(linRegRushYd)
## 
## Call:
## lm(formula = ryregform, data = trainTransformedry)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4869 -0.0828 -0.0119  0.0246  7.1651 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      2.344e-14  3.913e-03   0.000 1.000000    
## height          -2.408e-03  7.592e-03  -0.317 0.751079    
## weight           1.953e-03  7.115e-03   0.275 0.783686    
## cold_weather     1.400e-02  4.119e-03   3.399 0.000678 ***
## hot_weather     -1.387e-03  3.949e-03  -0.351 0.725333    
## home_team_1      1.003e-02  4.257e-03   2.357 0.018453 *  
## forty1          -1.549e-03  6.753e-03  -0.229 0.818571    
## vertical1       -1.878e-03  5.192e-03  -0.362 0.717597    
## ARI              4.434e-04  5.473e-03   0.081 0.935433    
## ATL              5.374e-04  5.500e-03   0.098 0.922157    
## BAL             -2.362e-03  5.504e-03  -0.429 0.667904    
## BUF             -1.553e-03  5.434e-03  -0.286 0.774986    
## CAR             -6.492e-03  5.398e-03  -1.203 0.229179    
## CHI             -2.772e-03  5.338e-03  -0.519 0.603544    
## CIN             -7.663e-04  5.436e-03  -0.141 0.887901    
## CLE              2.003e-03  5.411e-03   0.370 0.711216    
## DAL              1.735e-03  5.466e-03   0.317 0.750989    
## DEN              6.652e-03  5.487e-03   1.212 0.225401    
## DET              3.673e-03  5.411e-03   0.679 0.497292    
## GB              -4.934e-03  5.571e-03  -0.886 0.375822    
## HOU              5.347e-03  5.505e-03   0.971 0.331381    
## IND             -4.118e-03  5.465e-03  -0.754 0.451137    
## JAC             -1.431e-03  5.330e-03  -0.268 0.788321    
## KC               2.573e-04  5.447e-03   0.047 0.962318    
## MIA              2.191e-03  5.360e-03   0.409 0.682622    
## MINN            -1.518e-03  5.392e-03  -0.282 0.778260    
## NE              -1.918e-03  5.632e-03  -0.341 0.733407    
## NOR             -7.365e-03  5.614e-03  -1.312 0.189568    
## NYG              3.399e-03  5.488e-03   0.619 0.535628    
## NYJ             -6.759e-03  5.467e-03  -1.236 0.216349    
## OAK              3.653e-04  5.502e-03   0.066 0.947061    
## PHI             -2.417e-03  5.331e-03  -0.453 0.650336    
## PIT             -6.720e-03  5.471e-03  -1.228 0.219398    
## SD              -2.446e-03  5.369e-03  -0.456 0.648733    
## SEA             -5.358e-03  5.572e-03  -0.961 0.336316    
## STL              3.688e-03  5.423e-03   0.680 0.496463    
## TB               7.938e-04  5.372e-03   0.148 0.882546    
## TEN              2.142e-03  5.405e-03   0.396 0.691874    
## WAS              5.495e-03  5.434e-03   1.011 0.311876    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr   2.091e-03  4.997e-03   0.418 0.675637    
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr    7.585e-01  5.980e-03 126.854  < 2e-16 ***
## avg_rbry_pos     3.452e-03  6.967e-03   0.495 0.620259    
## avg_fuml_plyr    7.112e-04  5.780e-03   0.123 0.902077    
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -2.003e-06  6.279e-03   0.000 0.999745    
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -7.838e-03  4.502e-03  -1.741 0.081702 .  
## bad_weather_1    6.390e-03  3.980e-03   1.605 0.108436    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6487 on 27438 degrees of freedom
## Multiple R-squared:  0.5799, Adjusted R-squared:  0.5792 
## F-statistic: 841.6 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegRushYd2 <- update(linRegRushYd,~.-height-weight-hot_weather-home_team_1-is_WR-is_TE-forty1
                        -vertical1-ARI-ATL-BAL - BUF - CAR - CHI
                        -CIN - CLE - DAL - DEN - DET - GB - HOU - IND - JAC - KC - MIA 
                        -MINN - NE - NOR - NYG-NYJ - OAK - PHI - PIT -SD - SEA - STL 
                        -TB - TEN - WAS
                        -avg_rectd_plyr-avg_trg_team-avg_tdr_team-avg_rbra_team-avg_rbry_pos
                        -avg_fuml_team-avg_fuml_plyr-avg_qbints_team-avg_qbtdp_team
                        -avg_qbints_plyr-bad_weather_1-grass_1)

summary(linRegRushYd2)
## 
## Call:
## lm(formula = ry ~ cold_weather + avg_rbry_plyr + avg_qbtdp_plyr, 
##     data = trainTransformedry)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4564 -0.0775 -0.0072  0.0077  7.1706 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.343e-14  3.913e-03   0.000 1.000000    
## cold_weather    1.409e-02  3.913e-03   3.602 0.000316 ***
## avg_rbry_plyr   7.609e-01  3.913e-03 194.477  < 2e-16 ***
## avg_qbtdp_plyr -1.208e-03  3.913e-03  -0.309 0.757571    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6486 on 27480 degrees of freedom
## Multiple R-squared:  0.5793, Adjusted R-squared:  0.5793 
## F-statistic: 1.261e+04 on 3 and 27480 DF,  p-value: < 2.2e-16

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

RushydsPredicted <- predict(linRegRushYd2, newdata = testTransformedry)

SSEruyd <- sum((RushydsPredicted - testTransformedry$ry)^2)
SSTruyd <- sum((mean(nfl_data$ry)-testTransformedry$ry)^2)
r2_ruyd <- 1 - SSEruyd/SSTruyd 
r2_ruyd
## [1] 0.996394
rmse_ruyd <- sqrt(SSEruyd/nrow(testTransformedry))
rmse_ruyd
## [1] 0.6467476

Regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegRushYd2, which = c(1:3,5))

Summary statistics:

confint(linRegRushYd2)
##                       2.5 %      97.5 %
## (Intercept)    -0.007668979 0.007668979
## cold_weather    0.006424438 0.021762752
## avg_rbry_plyr   0.753270275 0.768608611
## avg_qbtdp_plyr -0.008876890 0.006461374
coef(summary(linRegRushYd2))
##                     Estimate  Std. Error       t value     Pr(>|t|)
## (Intercept)     2.343374e-14 0.003912644  5.989234e-12 1.0000000000
## cold_weather    1.409359e-02 0.003912735  3.601981e+00 0.0003163587
## avg_rbry_plyr   7.609394e-01 0.003912740  1.944774e+02 0.0000000000
## avg_qbtdp_plyr -1.207758e-03 0.003912722 -3.086747e-01 0.7575713455
anova(linRegRushYd2)
## Analysis of Variance Table
## 
## Response: ry
##                   Df  Sum Sq Mean Sq    F value    Pr(>F)    
## cold_weather       1     7.5     7.5    17.7329  2.55e-05 ***
## avg_rbry_plyr      1 15913.4 15913.4 37821.7831 < 2.2e-16 ***
## avg_qbtdp_plyr     1     0.0     0.0     0.0953    0.7576    
## Residuals      27480 11562.1     0.4                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_ry <- step(lm(ryregform, data = trainTransformedry), direction = "backward")
## Start:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-23744.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - avg_qbtdp_plyr  1       0.0 11546 -23746
## - KC              1       0.0 11546 -23746
## - OAK             1       0.0 11546 -23746
## - ARI             1       0.0 11546 -23746
## - ATL             1       0.0 11546 -23746
## - avg_fuml_plyr   1       0.0 11546 -23746
## - CIN             1       0.0 11546 -23746
## - TB              1       0.0 11546 -23746
## - forty1          1       0.0 11546 -23746
## - JAC             1       0.0 11546 -23746
## - weight          1       0.0 11546 -23746
## - MINN            1       0.0 11546 -23746
## - BUF             1       0.0 11546 -23746
## - height          1       0.0 11546 -23746
## - DAL             1       0.0 11546 -23746
## - NE              1       0.0 11546 -23746
## - hot_weather     1       0.1 11546 -23746
## - vertical1       1       0.1 11546 -23746
## - CLE             1       0.1 11546 -23746
## - TEN             1       0.1 11546 -23746
## - MIA             1       0.1 11546 -23746
## - avg_rectd_plyr  1       0.1 11546 -23746
## - BAL             1       0.1 11546 -23746
## - PHI             1       0.1 11546 -23746
## - SD              1       0.1 11546 -23746
## - avg_rbry_pos    1       0.1 11546 -23746
## - CHI             1       0.1 11546 -23746
## - NYG             1       0.2 11546 -23746
## - DET             1       0.2 11546 -23746
## - STL             1       0.2 11546 -23746
## - IND             1       0.2 11546 -23745
## - GB              1       0.3 11546 -23745
## - SEA             1       0.4 11546 -23745
## - HOU             1       0.4 11546 -23745
## - WAS             1       0.4 11546 -23745
## - CAR             1       0.6 11547 -23745
## - DEN             1       0.6 11547 -23745
## - PIT             1       0.6 11547 -23745
## - NYJ             1       0.6 11547 -23745
## - NOR             1       0.7 11547 -23744
## <none>                        11546 -23744
## - bad_weather_1   1       1.1 11547 -23743
## - grass_1         1       1.3 11547 -23743
## - home_team_1     1       2.3 11548 -23740
## - cold_weather    1       4.9 11551 -23734
## - avg_rbry_plyr   1    6771.6 18318 -11062
## 
## Step:  AIC=-23746.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - KC              1       0.0 11546 -23748
## - OAK             1       0.0 11546 -23748
## - ARI             1       0.0 11546 -23748
## - ATL             1       0.0 11546 -23748
## - CIN             1       0.0 11546 -23748
## - TB              1       0.0 11546 -23748
## - avg_fuml_plyr   1       0.0 11546 -23748
## - forty1          1       0.0 11546 -23748
## - JAC             1       0.0 11546 -23748
## - MINN            1       0.0 11546 -23748
## - weight          1       0.0 11546 -23748
## - BUF             1       0.0 11546 -23748
## - DAL             1       0.0 11546 -23748
## - height          1       0.0 11546 -23748
## - NE              1       0.0 11546 -23748
## - hot_weather     1       0.1 11546 -23748
## - vertical1       1       0.1 11546 -23748
## - CLE             1       0.1 11546 -23748
## - TEN             1       0.1 11546 -23748
## - MIA             1       0.1 11546 -23748
## - BAL             1       0.1 11546 -23748
## - avg_rectd_plyr  1       0.1 11546 -23748
## - PHI             1       0.1 11546 -23748
## - SD              1       0.1 11546 -23748
## - avg_rbry_pos    1       0.1 11546 -23748
## - CHI             1       0.1 11546 -23748
## - NYG             1       0.2 11546 -23748
## - DET             1       0.2 11546 -23748
## - STL             1       0.2 11546 -23748
## - IND             1       0.2 11546 -23747
## - GB              1       0.3 11546 -23747
## - SEA             1       0.4 11546 -23747
## - HOU             1       0.4 11546 -23747
## - WAS             1       0.4 11546 -23747
## - CAR             1       0.6 11547 -23747
## - DEN             1       0.6 11547 -23747
## - PIT             1       0.6 11547 -23747
## - NYJ             1       0.6 11547 -23747
## - NOR             1       0.7 11547 -23746
## <none>                        11546 -23746
## - bad_weather_1   1       1.1 11547 -23745
## - grass_1         1       1.3 11547 -23745
## - home_team_1     1       2.3 11548 -23742
## - cold_weather    1       4.9 11551 -23736
## - avg_rbry_plyr   1    6897.6 18444 -10875
## 
## Step:  AIC=-23748.01
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - OAK             1       0.0 11546 -23750
## - ARI             1       0.0 11546 -23750
## - ATL             1       0.0 11546 -23750
## - TB              1       0.0 11546 -23750
## - avg_fuml_plyr   1       0.0 11546 -23750
## - CIN             1       0.0 11546 -23750
## - forty1          1       0.0 11546 -23750
## - weight          1       0.0 11546 -23750
## - height          1       0.0 11546 -23750
## - JAC             1       0.0 11546 -23750
## - DAL             1       0.0 11546 -23750
## - MINN            1       0.1 11546 -23750
## - hot_weather     1       0.1 11546 -23750
## - BUF             1       0.1 11546 -23750
## - vertical1       1       0.1 11546 -23750
## - CLE             1       0.1 11546 -23750
## - NE              1       0.1 11546 -23750
## - avg_rectd_plyr  1       0.1 11546 -23750
## - TEN             1       0.1 11546 -23750
## - MIA             1       0.1 11546 -23750
## - avg_rbry_pos    1       0.1 11546 -23750
## - BAL             1       0.1 11546 -23750
## - PHI             1       0.1 11546 -23750
## - SD              1       0.1 11546 -23750
## - CHI             1       0.2 11546 -23750
## - NYG             1       0.2 11546 -23750
## - DET             1       0.2 11546 -23749
## - STL             1       0.2 11546 -23749
## - IND             1       0.3 11546 -23749
## - GB              1       0.5 11546 -23749
## - HOU             1       0.5 11546 -23749
## - SEA             1       0.5 11546 -23749
## - WAS             1       0.5 11546 -23749
## - DEN             1       0.8 11547 -23748
## - CAR             1       0.8 11547 -23748
## <none>                        11546 -23748
## - NYJ             1       0.9 11547 -23748
## - PIT             1       0.9 11547 -23748
## - NOR             1       1.0 11547 -23748
## - bad_weather_1   1       1.1 11547 -23747
## - grass_1         1       1.3 11547 -23747
## - home_team_1     1       2.3 11548 -23744
## - cold_weather    1       4.9 11551 -23738
## - avg_rbry_plyr   1    6898.0 18444 -10876
## 
## Step:  AIC=-23750
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - ARI             1       0.0 11546 -23752
## - ATL             1       0.0 11546 -23752
## - TB              1       0.0 11546 -23752
## - avg_fuml_plyr   1       0.0 11546 -23752
## - CIN             1       0.0 11546 -23752
## - forty1          1       0.0 11546 -23752
## - weight          1       0.0 11546 -23752
## - height          1       0.0 11546 -23752
## - DAL             1       0.0 11546 -23752
## - hot_weather     1       0.1 11546 -23752
## - vertical1       1       0.1 11546 -23752
## - JAC             1       0.1 11546 -23752
## - MINN            1       0.1 11546 -23752
## - BUF             1       0.1 11546 -23752
## - CLE             1       0.1 11546 -23752
## - avg_rectd_plyr  1       0.1 11546 -23752
## - TEN             1       0.1 11546 -23752
## - MIA             1       0.1 11546 -23752
## - NE              1       0.1 11546 -23752
## - avg_rbry_pos    1       0.1 11546 -23752
## - BAL             1       0.1 11546 -23752
## - PHI             1       0.1 11546 -23752
## - SD              1       0.1 11546 -23752
## - CHI             1       0.2 11546 -23752
## - NYG             1       0.2 11546 -23752
## - DET             1       0.3 11546 -23751
## - STL             1       0.3 11546 -23751
## - IND             1       0.4 11546 -23751
## - HOU             1       0.5 11546 -23751
## - GB              1       0.5 11546 -23751
## - WAS             1       0.6 11547 -23751
## - SEA             1       0.6 11547 -23751
## <none>                        11546 -23750
## - DEN             1       0.9 11547 -23750
## - CAR             1       1.0 11547 -23750
## - NYJ             1       1.0 11547 -23750
## - PIT             1       1.0 11547 -23750
## - bad_weather_1   1       1.1 11547 -23749
## - NOR             1       1.1 11547 -23749
## - grass_1         1       1.3 11547 -23749
## - home_team_1     1       2.3 11548 -23746
## - cold_weather    1       4.9 11551 -23740
## - avg_rbry_plyr   1    6907.2 18453 -10865
## 
## Step:  AIC=-23752
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ATL + BAL + BUF + CAR + CHI + CIN + 
##     CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - ATL             1       0.0 11546 -23754
## - TB              1       0.0 11546 -23754
## - avg_fuml_plyr   1       0.0 11546 -23754
## - CIN             1       0.0 11546 -23754
## - forty1          1       0.0 11546 -23754
## - weight          1       0.0 11546 -23754
## - height          1       0.0 11546 -23754
## - DAL             1       0.0 11546 -23754
## - hot_weather     1       0.1 11546 -23754
## - vertical1       1       0.1 11546 -23754
## - JAC             1       0.1 11546 -23754
## - CLE             1       0.1 11546 -23754
## - MINN            1       0.1 11546 -23754
## - BUF             1       0.1 11546 -23754
## - avg_rectd_plyr  1       0.1 11546 -23754
## - TEN             1       0.1 11546 -23754
## - MIA             1       0.1 11546 -23754
## - NE              1       0.1 11546 -23754
## - avg_rbry_pos    1       0.1 11546 -23754
## - BAL             1       0.2 11546 -23754
## - PHI             1       0.2 11546 -23754
## - SD              1       0.2 11546 -23754
## - CHI             1       0.2 11546 -23754
## - NYG             1       0.2 11546 -23754
## - DET             1       0.3 11546 -23753
## - STL             1       0.3 11546 -23753
## - IND             1       0.4 11546 -23753
## - HOU             1       0.6 11546 -23753
## - GB              1       0.6 11547 -23753
## - WAS             1       0.6 11547 -23753
## - SEA             1       0.7 11547 -23752
## <none>                        11546 -23752
## - DEN             1       0.9 11547 -23752
## - CAR             1       1.0 11547 -23752
## - bad_weather_1   1       1.1 11547 -23751
## - NYJ             1       1.1 11547 -23751
## - PIT             1       1.1 11547 -23751
## - NOR             1       1.3 11547 -23751
## - grass_1         1       1.3 11547 -23751
## - home_team_1     1       2.4 11548 -23748
## - cold_weather    1       4.9 11551 -23742
## - avg_rbry_plyr   1    6911.8 18458 -10860
## 
## Step:  AIC=-23754
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - TB              1       0.0 11546 -23756
## - avg_fuml_plyr   1       0.0 11546 -23756
## - forty1          1       0.0 11546 -23756
## - CIN             1       0.0 11546 -23756
## - weight          1       0.0 11546 -23756
## - height          1       0.0 11546 -23756
## - DAL             1       0.0 11546 -23756
## - hot_weather     1       0.1 11546 -23756
## - vertical1       1       0.1 11546 -23756
## - CLE             1       0.1 11546 -23756
## - JAC             1       0.1 11546 -23756
## - MINN            1       0.1 11546 -23756
## - avg_rectd_plyr  1       0.1 11546 -23756
## - TEN             1       0.1 11546 -23756
## - BUF             1       0.1 11546 -23756
## - MIA             1       0.1 11546 -23756
## - avg_rbry_pos    1       0.1 11546 -23756
## - NE              1       0.1 11546 -23756
## - BAL             1       0.2 11546 -23756
## - PHI             1       0.2 11546 -23756
## - SD              1       0.2 11546 -23756
## - NYG             1       0.2 11546 -23756
## - CHI             1       0.2 11546 -23756
## - DET             1       0.3 11546 -23755
## - STL             1       0.3 11546 -23755
## - IND             1       0.5 11546 -23755
## - HOU             1       0.6 11546 -23755
## - WAS             1       0.6 11547 -23755
## - GB              1       0.6 11547 -23755
## - SEA             1       0.7 11547 -23754
## <none>                        11546 -23754
## - DEN             1       0.9 11547 -23754
## - bad_weather_1   1       1.1 11547 -23753
## - CAR             1       1.1 11547 -23753
## - PIT             1       1.1 11547 -23753
## - NYJ             1       1.1 11547 -23753
## - grass_1         1       1.3 11547 -23753
## - NOR             1       1.4 11547 -23753
## - home_team_1     1       2.4 11548 -23750
## - cold_weather    1       4.9 11551 -23744
## - avg_rbry_plyr   1    6912.0 18458 -10862
## 
## Step:  AIC=-23755.98
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - avg_fuml_plyr   1       0.0 11546 -23758
## - forty1          1       0.0 11546 -23758
## - CIN             1       0.0 11546 -23758
## - weight          1       0.0 11546 -23758
## - DAL             1       0.0 11546 -23758
## - height          1       0.0 11546 -23758
## - hot_weather     1       0.1 11546 -23758
## - vertical1       1       0.1 11546 -23758
## - CLE             1       0.1 11546 -23758
## - TEN             1       0.1 11546 -23758
## - avg_rectd_plyr  1       0.1 11546 -23758
## - JAC             1       0.1 11546 -23758
## - MIA             1       0.1 11546 -23758
## - MINN            1       0.1 11546 -23758
## - BUF             1       0.1 11546 -23758
## - avg_rbry_pos    1       0.1 11546 -23758
## - NE              1       0.1 11546 -23758
## - BAL             1       0.2 11546 -23758
## - PHI             1       0.2 11546 -23758
## - SD              1       0.2 11546 -23758
## - NYG             1       0.2 11546 -23758
## - CHI             1       0.2 11546 -23757
## - DET             1       0.3 11546 -23757
## - STL             1       0.3 11546 -23757
## - IND             1       0.5 11546 -23757
## - HOU             1       0.6 11546 -23757
## - WAS             1       0.6 11547 -23757
## - GB              1       0.7 11547 -23756
## - SEA             1       0.8 11547 -23756
## <none>                        11546 -23756
## - DEN             1       0.9 11547 -23756
## - bad_weather_1   1       1.1 11547 -23755
## - CAR             1       1.1 11547 -23755
## - PIT             1       1.2 11547 -23755
## - NYJ             1       1.2 11547 -23755
## - grass_1         1       1.3 11547 -23755
## - NOR             1       1.4 11547 -23755
## - home_team_1     1       2.4 11548 -23752
## - cold_weather    1       4.9 11551 -23746
## - avg_rbry_plyr   1    6912.0 18458 -10864
## 
## Step:  AIC=-23757.96
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - forty1          1       0.0 11546 -23759.9
## - weight          1       0.0 11546 -23759.9
## - CIN             1       0.0 11546 -23759.9
## - height          1       0.0 11546 -23759.9
## - DAL             1       0.0 11546 -23759.9
## - hot_weather     1       0.1 11546 -23759.8
## - vertical1       1       0.1 11546 -23759.8
## - CLE             1       0.1 11546 -23759.8
## - avg_rectd_plyr  1       0.1 11546 -23759.8
## - TEN             1       0.1 11546 -23759.8
## - JAC             1       0.1 11546 -23759.8
## - MIA             1       0.1 11546 -23759.8
## - MINN            1       0.1 11546 -23759.8
## - BUF             1       0.1 11546 -23759.7
## - avg_rbry_pos    1       0.1 11546 -23759.7
## - NE              1       0.1 11546 -23759.7
## - BAL             1       0.2 11546 -23759.5
## - PHI             1       0.2 11546 -23759.5
## - SD              1       0.2 11546 -23759.5
## - NYG             1       0.2 11546 -23759.5
## - CHI             1       0.2 11546 -23759.4
## - STL             1       0.3 11546 -23759.3
## - DET             1       0.3 11546 -23759.3
## - IND             1       0.5 11546 -23758.8
## - HOU             1       0.6 11547 -23758.6
## - WAS             1       0.6 11547 -23758.5
## - GB              1       0.7 11547 -23758.4
## - SEA             1       0.8 11547 -23758.1
## <none>                        11546 -23758.0
## - DEN             1       0.9 11547 -23757.7
## - bad_weather_1   1       1.1 11547 -23757.4
## - CAR             1       1.1 11547 -23757.2
## - PIT             1       1.2 11547 -23757.1
## - NYJ             1       1.2 11547 -23757.1
## - grass_1         1       1.3 11547 -23756.8
## - NOR             1       1.4 11547 -23756.6
## - home_team_1     1       2.4 11548 -23754.3
## - cold_weather    1       4.9 11551 -23748.4
## - avg_rbry_plyr   1    7680.5 19227  -9744.5
## 
## Step:  AIC=-23759.92
## ry ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     vertical1 + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - weight          1       0.0 11546 -23761.9
## - CIN             1       0.0 11546 -23761.8
## - vertical1       1       0.0 11546 -23761.8
## - DAL             1       0.0 11546 -23761.8
## - height          1       0.0 11546 -23761.8
## - hot_weather     1       0.1 11546 -23761.8
## - CLE             1       0.1 11546 -23761.8
## - TEN             1       0.1 11546 -23761.7
## - MIA             1       0.1 11546 -23761.7
## - JAC             1       0.1 11546 -23761.7
## - BUF             1       0.1 11546 -23761.7
## - MINN            1       0.1 11546 -23761.7
## - avg_rectd_plyr  1       0.1 11546 -23761.7
## - avg_rbry_pos    1       0.1 11546 -23761.7
## - NE              1       0.1 11546 -23761.6
## - BAL             1       0.2 11546 -23761.5
## - PHI             1       0.2 11546 -23761.5
## - SD              1       0.2 11546 -23761.4
## - NYG             1       0.2 11546 -23761.4
## - CHI             1       0.2 11546 -23761.4
## - DET             1       0.3 11546 -23761.3
## - STL             1       0.3 11546 -23761.3
## - IND             1       0.5 11546 -23760.8
## - HOU             1       0.6 11547 -23760.6
## - WAS             1       0.6 11547 -23760.4
## - GB              1       0.7 11547 -23760.3
## - SEA             1       0.8 11547 -23760.1
## <none>                        11546 -23759.9
## - DEN             1       0.9 11547 -23759.7
## - bad_weather_1   1       1.1 11547 -23759.3
## - CAR             1       1.1 11547 -23759.2
## - PIT             1       1.2 11547 -23759.0
## - NYJ             1       1.2 11547 -23759.0
## - grass_1         1       1.3 11547 -23758.8
## - NOR             1       1.4 11547 -23758.5
## - home_team_1     1       2.4 11548 -23756.2
## - cold_weather    1       4.9 11551 -23750.3
## - avg_rbry_plyr   1    7878.2 19424  -9465.3
## 
## Step:  AIC=-23761.88
## ry ~ height + cold_weather + hot_weather + home_team_1 + vertical1 + 
##     BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + 
##     HOU + IND + JAC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + 
##     PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - height          1       0.0 11546 -23763.8
## - CIN             1       0.0 11546 -23763.8
## - DAL             1       0.0 11546 -23763.8
## - vertical1       1       0.0 11546 -23763.8
## - hot_weather     1       0.1 11546 -23763.8
## - CLE             1       0.1 11546 -23763.7
## - TEN             1       0.1 11546 -23763.7
## - MIA             1       0.1 11546 -23763.7
## - JAC             1       0.1 11546 -23763.7
## - BUF             1       0.1 11546 -23763.7
## - MINN            1       0.1 11546 -23763.7
## - avg_rectd_plyr  1       0.1 11546 -23763.6
## - NE              1       0.1 11546 -23763.5
## - avg_rbry_pos    1       0.2 11546 -23763.5
## - BAL             1       0.2 11546 -23763.4
## - PHI             1       0.2 11546 -23763.4
## - SD              1       0.2 11546 -23763.4
## - NYG             1       0.2 11546 -23763.4
## - CHI             1       0.2 11546 -23763.3
## - DET             1       0.3 11546 -23763.3
## - STL             1       0.3 11546 -23763.3
## - IND             1       0.5 11546 -23762.7
## - HOU             1       0.6 11547 -23762.5
## - WAS             1       0.6 11547 -23762.3
## - GB              1       0.7 11547 -23762.3
## - SEA             1       0.8 11547 -23762.0
## <none>                        11546 -23761.9
## - DEN             1       0.9 11547 -23761.7
## - bad_weather_1   1       1.1 11547 -23761.3
## - CAR             1       1.1 11547 -23761.2
## - PIT             1       1.2 11547 -23761.0
## - NYJ             1       1.2 11547 -23761.0
## - grass_1         1       1.3 11547 -23760.7
## - NOR             1       1.4 11547 -23760.5
## - home_team_1     1       2.4 11548 -23758.2
## - cold_weather    1       4.9 11551 -23752.3
## - avg_rbry_plyr   1    7904.9 19451  -9429.5
## 
## Step:  AIC=-23763.8
## ry ~ cold_weather + hot_weather + home_team_1 + vertical1 + BAL + 
##     BUF + CAR + CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + 
##     IND + JAC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + PIT + 
##     SD + SEA + STL + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS    AIC
## - vertical1       1       0.0 11546 -23766
## - CIN             1       0.0 11546 -23766
## - DAL             1       0.0 11546 -23766
## - hot_weather     1       0.1 11546 -23766
## - CLE             1       0.1 11546 -23766
## - TEN             1       0.1 11546 -23766
## - MIA             1       0.1 11546 -23766
## - JAC             1       0.1 11546 -23766
## - BUF             1       0.1 11546 -23766
## - MINN            1       0.1 11546 -23766
## - avg_rectd_plyr  1       0.1 11546 -23766
## - NE              1       0.1 11546 -23766
## - PHI             1       0.2 11546 -23765
## - BAL             1       0.2 11546 -23765
## - NYG             1       0.2 11546 -23765
## - SD              1       0.2 11546 -23765
## - CHI             1       0.2 11546 -23765
## - avg_rbry_pos    1       0.3 11546 -23765
## - DET             1       0.3 11546 -23765
## - STL             1       0.3 11546 -23765
## - IND             1       0.5 11546 -23765
## - HOU             1       0.6 11547 -23765
## - WAS             1       0.7 11547 -23764
## - GB              1       0.7 11547 -23764
## - SEA             1       0.8 11547 -23764
## <none>                        11546 -23764
## - DEN             1       0.9 11547 -23764
## - bad_weather_1   1       1.1 11547 -23763
## - CAR             1       1.1 11547 -23763
## - PIT             1       1.2 11547 -23763
## - NYJ             1       1.2 11547 -23763
## - grass_1         1       1.3 11547 -23763
## - NOR             1       1.4 11548 -23762
## - home_team_1     1       2.4 11548 -23760
## - cold_weather    1       4.9 11551 -23754
## - avg_rbry_plyr   1    7905.2 19451  -9431
## 
## Step:  AIC=-23765.73
## ry ~ cold_weather + hot_weather + home_team_1 + BAL + BUF + CAR + 
##     CHI + CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + 
##     STL + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - CIN             1       0.0 11546 -23767.6
## - DAL             1       0.0 11546 -23767.6
## - hot_weather     1       0.1 11546 -23767.6
## - CLE             1       0.1 11546 -23767.6
## - TEN             1       0.1 11546 -23767.6
## - avg_rectd_plyr  1       0.1 11546 -23767.5
## - MIA             1       0.1 11546 -23767.5
## - JAC             1       0.1 11546 -23767.5
## - BUF             1       0.1 11546 -23767.5
## - MINN            1       0.1 11546 -23767.5
## - NE              1       0.1 11546 -23767.4
## - PHI             1       0.2 11546 -23767.3
## - BAL             1       0.2 11546 -23767.3
## - SD              1       0.2 11546 -23767.2
## - NYG             1       0.2 11546 -23767.2
## - CHI             1       0.2 11546 -23767.2
## - DET             1       0.2 11546 -23767.1
## - avg_rbry_pos    1       0.3 11546 -23767.1
## - STL             1       0.3 11546 -23767.1
## - IND             1       0.5 11547 -23766.6
## - HOU             1       0.6 11547 -23766.4
## - WAS             1       0.7 11547 -23766.2
## - GB              1       0.7 11547 -23766.2
## - SEA             1       0.8 11547 -23765.9
## <none>                        11546 -23765.7
## - DEN             1       0.9 11547 -23765.5
## - bad_weather_1   1       1.1 11547 -23765.2
## - CAR             1       1.1 11547 -23765.0
## - PIT             1       1.2 11547 -23764.9
## - NYJ             1       1.2 11547 -23764.8
## - grass_1         1       1.3 11547 -23764.6
## - NOR             1       1.4 11548 -23764.3
## - home_team_1     1       2.4 11548 -23762.1
## - cold_weather    1       4.9 11551 -23756.1
## - avg_rbry_plyr   1    7918.4 19465  -9414.3
## 
## Step:  AIC=-23767.65
## ry ~ cold_weather + hot_weather + home_team_1 + BAL + BUF + CAR + 
##     CHI + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + MIA + 
##     MINN + NE + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - hot_weather     1       0.1 11546 -23769.5
## - DAL             1       0.1 11546 -23769.5
## - CLE             1       0.1 11546 -23769.5
## - BUF             1       0.1 11546 -23769.5
## - JAC             1       0.1 11546 -23769.5
## - avg_rectd_plyr  1       0.1 11546 -23769.5
## - MINN            1       0.1 11546 -23769.4
## - TEN             1       0.1 11546 -23769.4
## - MIA             1       0.1 11546 -23769.4
## - NE              1       0.1 11546 -23769.4
## - BAL             1       0.2 11546 -23769.3
## - PHI             1       0.2 11546 -23769.3
## - SD              1       0.2 11546 -23769.2
## - CHI             1       0.2 11546 -23769.1
## - NYG             1       0.2 11546 -23769.1
## - avg_rbry_pos    1       0.3 11546 -23769.0
## - DET             1       0.3 11546 -23769.0
## - STL             1       0.3 11546 -23768.9
## - IND             1       0.5 11547 -23768.6
## - HOU             1       0.6 11547 -23768.2
## - GB              1       0.6 11547 -23768.1
## - WAS             1       0.7 11547 -23767.9
## - SEA             1       0.7 11547 -23767.9
## <none>                        11546 -23767.6
## - DEN             1       1.0 11547 -23767.3
## - bad_weather_1   1       1.1 11547 -23767.1
## - CAR             1       1.1 11547 -23767.0
## - PIT             1       1.2 11547 -23766.9
## - NYJ             1       1.2 11547 -23766.8
## - grass_1         1       1.3 11547 -23766.6
## - NOR             1       1.4 11548 -23766.3
## - home_team_1     1       2.4 11548 -23764.0
## - cold_weather    1       4.8 11551 -23758.1
## - avg_rbry_plyr   1    7920.9 19467  -9412.7
## 
## Step:  AIC=-23769.52
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - DAL             1       0.1 11546 -23771.4
## - JAC             1       0.1 11546 -23771.3
## - CLE             1       0.1 11546 -23771.3
## - BUF             1       0.1 11546 -23771.3
## - avg_rectd_plyr  1       0.1 11546 -23771.3
## - MINN            1       0.1 11546 -23771.3
## - TEN             1       0.1 11546 -23771.3
## - MIA             1       0.1 11546 -23771.3
## - NE              1       0.1 11546 -23771.3
## - PHI             1       0.2 11546 -23771.1
## - BAL             1       0.2 11546 -23771.1
## - SD              1       0.2 11546 -23771.1
## - CHI             1       0.2 11546 -23771.0
## - NYG             1       0.2 11546 -23770.9
## - avg_rbry_pos    1       0.3 11546 -23770.9
## - DET             1       0.3 11546 -23770.9
## - STL             1       0.3 11546 -23770.8
## - IND             1       0.5 11547 -23770.4
## - HOU             1       0.6 11547 -23770.1
## - GB              1       0.6 11547 -23770.0
## - WAS             1       0.7 11547 -23769.8
## - SEA             1       0.8 11547 -23769.7
## <none>                        11546 -23769.5
## - DEN             1       1.0 11547 -23769.2
## - bad_weather_1   1       1.1 11547 -23769.0
## - CAR             1       1.1 11547 -23768.9
## - PIT             1       1.2 11547 -23768.7
## - NYJ             1       1.2 11547 -23768.6
## - grass_1         1       1.3 11548 -23768.3
## - NOR             1       1.4 11548 -23768.2
## - home_team_1     1       2.4 11548 -23765.9
## - cold_weather    1       4.9 11551 -23759.9
## - avg_rbry_plyr   1    7921.2 19467  -9414.3
## 
## Step:  AIC=-23771.4
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + CLE + 
##     DEN + DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + 
##     NYG + NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - CLE             1       0.1 11546 -23773.2
## - TEN             1       0.1 11546 -23773.2
## - avg_rectd_plyr  1       0.1 11546 -23773.2
## - MIA             1       0.1 11546 -23773.2
## - JAC             1       0.1 11546 -23773.2
## - BUF             1       0.1 11546 -23773.2
## - MINN            1       0.1 11546 -23773.1
## - NE              1       0.1 11546 -23773.1
## - PHI             1       0.2 11546 -23773.0
## - BAL             1       0.2 11546 -23772.9
## - SD              1       0.2 11546 -23772.9
## - NYG             1       0.2 11546 -23772.9
## - CHI             1       0.2 11546 -23772.8
## - DET             1       0.3 11546 -23772.8
## - avg_rbry_pos    1       0.3 11546 -23772.8
## - STL             1       0.3 11546 -23772.8
## - IND             1       0.5 11547 -23772.2
## - HOU             1       0.6 11547 -23772.0
## - WAS             1       0.7 11547 -23771.8
## - GB              1       0.7 11547 -23771.8
## - SEA             1       0.8 11547 -23771.4
## <none>                        11546 -23771.4
## - DEN             1       0.9 11547 -23771.1
## - bad_weather_1   1       1.1 11547 -23770.8
## - CAR             1       1.2 11547 -23770.6
## - PIT             1       1.2 11548 -23770.4
## - NYJ             1       1.3 11548 -23770.3
## - grass_1         1       1.4 11548 -23770.1
## - NOR             1       1.5 11548 -23769.8
## - home_team_1     1       2.3 11548 -23767.9
## - cold_weather    1       4.9 11551 -23761.8
## - avg_rbry_plyr   1    7923.9 19470  -9412.3
## 
## Step:  AIC=-23773.25
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN + 
##     DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + PHI + PIT + SD + SEA + STL + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - TEN             1       0.1 11546 -23775.1
## - MIA             1       0.1 11546 -23775.1
## - avg_rectd_plyr  1       0.1 11546 -23775.1
## - JAC             1       0.1 11546 -23775.0
## - BUF             1       0.1 11546 -23775.0
## - MINN            1       0.1 11546 -23775.0
## - NE              1       0.2 11546 -23774.9
## - NYG             1       0.2 11546 -23774.8
## - PHI             1       0.2 11546 -23774.7
## - BAL             1       0.2 11546 -23774.7
## - DET             1       0.2 11546 -23774.7
## - STL             1       0.2 11546 -23774.7
## - SD              1       0.2 11546 -23774.7
## - avg_rbry_pos    1       0.3 11546 -23774.6
## - CHI             1       0.3 11547 -23774.6
## - HOU             1       0.5 11547 -23774.0
## - IND             1       0.6 11547 -23773.9
## - WAS             1       0.6 11547 -23773.7
## - GB              1       0.7 11547 -23773.5
## <none>                        11546 -23773.2
## - SEA             1       0.9 11547 -23773.1
## - DEN             1       0.9 11547 -23773.1
## - bad_weather_1   1       1.1 11547 -23772.6
## - CAR             1       1.3 11548 -23772.3
## - PIT             1       1.3 11548 -23772.1
## - grass_1         1       1.4 11548 -23772.0
## - NYJ             1       1.4 11548 -23771.9
## - NOR             1       1.6 11548 -23771.4
## - home_team_1     1       2.4 11549 -23769.6
## - cold_weather    1       5.0 11551 -23763.4
## - avg_rbry_plyr   1    7923.9 19470  -9414.2
## 
## Step:  AIC=-23775.11
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN + 
##     DET + GB + HOU + IND + JAC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + PHI + PIT + SD + SEA + STL + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - MIA             1       0.1 11546 -23777.0
## - avg_rectd_plyr  1       0.1 11546 -23776.9
## - JAC             1       0.1 11546 -23776.8
## - BUF             1       0.1 11546 -23776.8
## - MINN            1       0.1 11546 -23776.8
## - NE              1       0.2 11546 -23776.7
## - NYG             1       0.2 11546 -23776.7
## - DET             1       0.2 11547 -23776.6
## - STL             1       0.2 11547 -23776.6
## - PHI             1       0.2 11547 -23776.5
## - BAL             1       0.2 11547 -23776.5
## - avg_rbry_pos    1       0.2 11547 -23776.5
## - SD              1       0.3 11547 -23776.4
## - CHI             1       0.3 11547 -23776.4
## - HOU             1       0.5 11547 -23775.9
## - IND             1       0.6 11547 -23775.7
## - WAS             1       0.6 11547 -23775.7
## - GB              1       0.8 11547 -23775.2
## <none>                        11546 -23775.1
## - DEN             1       0.9 11547 -23775.1
## - SEA             1       0.9 11547 -23774.8
## - bad_weather_1   1       1.1 11547 -23774.5
## - CAR             1       1.3 11548 -23773.9
## - grass_1         1       1.3 11548 -23773.9
## - PIT             1       1.4 11548 -23773.7
## - NYJ             1       1.5 11548 -23773.6
## - NOR             1       1.7 11548 -23773.1
## - home_team_1     1       2.4 11549 -23771.4
## - cold_weather    1       5.0 11551 -23765.2
## - avg_rbry_plyr   1    7924.1 19471  -9415.9
## 
## Step:  AIC=-23776.97
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN + 
##     DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYG + NYJ + 
##     PHI + PIT + SD + SEA + STL + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS      AIC
## - avg_rectd_plyr  1       0.1 11546 -23778.8
## - JAC             1       0.1 11546 -23778.6
## - BUF             1       0.1 11546 -23778.6
## - MINN            1       0.2 11547 -23778.6
## - NYG             1       0.2 11547 -23778.6
## - NE              1       0.2 11547 -23778.5
## - DET             1       0.2 11547 -23778.5
## - STL             1       0.2 11547 -23778.5
## - avg_rbry_pos    1       0.3 11547 -23778.4
## - PHI             1       0.3 11547 -23778.3
## - BAL             1       0.3 11547 -23778.3
## - SD              1       0.3 11547 -23778.2
## - CHI             1       0.3 11547 -23778.2
## - HOU             1       0.5 11547 -23777.8
## - WAS             1       0.6 11547 -23777.6
## - IND             1       0.6 11547 -23777.5
## - DEN             1       0.8 11547 -23777.0
## <none>                        11546 -23777.0
## - GB              1       0.8 11547 -23776.9
## - SEA             1       1.0 11547 -23776.6
## - bad_weather_1   1       1.1 11548 -23776.4
## - grass_1         1       1.3 11548 -23775.8
## - CAR             1       1.4 11548 -23775.6
## - PIT             1       1.5 11548 -23775.4
## - NYJ             1       1.5 11548 -23775.3
## - NOR             1       1.7 11548 -23774.8
## - home_team_1     1       2.4 11549 -23773.2
## - cold_weather    1       5.0 11551 -23767.1
## - avg_rbry_plyr   1    7925.1 19472  -9416.4
## 
## Step:  AIC=-23778.78
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN + 
##     DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYG + NYJ + 
##     PHI + PIT + SD + SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - JAC            1       0.1 11547 -23780.4
## - BUF            1       0.1 11547 -23780.4
## - MINN           1       0.2 11547 -23780.4
## - NYG            1       0.2 11547 -23780.4
## - NE             1       0.2 11547 -23780.4
## - avg_rbry_pos   1       0.2 11547 -23780.3
## - STL            1       0.2 11547 -23780.3
## - DET            1       0.2 11547 -23780.3
## - PHI            1       0.3 11547 -23780.2
## - BAL            1       0.3 11547 -23780.1
## - SD             1       0.3 11547 -23780.1
## - CHI            1       0.3 11547 -23780.0
## - HOU            1       0.5 11547 -23779.6
## - WAS            1       0.6 11547 -23779.4
## - IND            1       0.6 11547 -23779.3
## - GB             1       0.8 11547 -23778.9
## <none>                       11546 -23778.8
## - DEN            1       0.9 11547 -23778.8
## - SEA            1       1.0 11548 -23778.4
## - bad_weather_1  1       1.1 11548 -23778.2
## - grass_1        1       1.3 11548 -23777.6
## - CAR            1       1.4 11548 -23777.5
## - PIT            1       1.5 11548 -23777.3
## - NYJ            1       1.5 11548 -23777.1
## - NOR            1       1.7 11548 -23776.7
## - home_team_1    1       2.4 11549 -23775.0
## - cold_weather   1       5.0 11551 -23769.0
## - avg_rbry_plyr  1    7948.1 19495  -9385.8
## 
## Step:  AIC=-23780.44
## ry ~ cold_weather + home_team_1 + BAL + BUF + CAR + CHI + DEN + 
##     DET + GB + HOU + IND + MINN + NE + NOR + NYG + NYJ + PHI + 
##     PIT + SD + SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - BUF            1       0.1 11547 -23782.1
## - MINN           1       0.1 11547 -23782.1
## - NE             1       0.2 11547 -23782.1
## - avg_rbry_pos   1       0.2 11547 -23782.0
## - NYG            1       0.2 11547 -23782.0
## - STL            1       0.2 11547 -23781.9
## - PHI            1       0.2 11547 -23781.9
## - DET            1       0.2 11547 -23781.9
## - BAL            1       0.2 11547 -23781.9
## - SD             1       0.3 11547 -23781.8
## - CHI            1       0.3 11547 -23781.7
## - HOU            1       0.5 11547 -23781.2
## - IND            1       0.6 11547 -23781.1
## - WAS            1       0.6 11547 -23780.9
## - GB             1       0.8 11547 -23780.6
## <none>                       11547 -23780.4
## - DEN            1       0.9 11548 -23780.2
## - SEA            1       0.9 11548 -23780.2
## - bad_weather_1  1       1.1 11548 -23779.9
## - CAR            1       1.3 11548 -23779.3
## - grass_1        1       1.4 11548 -23779.2
## - PIT            1       1.4 11548 -23779.1
## - NYJ            1       1.5 11548 -23778.9
## - NOR            1       1.6 11548 -23778.6
## - home_team_1    1       2.4 11549 -23776.8
## - cold_weather   1       5.0 11552 -23770.5
## - avg_rbry_plyr  1    7948.4 19495  -9387.3
## 
## Step:  AIC=-23782.13
## ry ~ cold_weather + home_team_1 + BAL + CAR + CHI + DEN + DET + 
##     GB + HOU + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + 
##     SD + SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - MINN           1       0.1 11547 -23783.8
## - NE             1       0.1 11547 -23783.8
## - avg_rbry_pos   1       0.2 11547 -23783.7
## - PHI            1       0.2 11547 -23783.6
## - BAL            1       0.2 11547 -23783.6
## - NYG            1       0.2 11547 -23783.6
## - SD             1       0.2 11547 -23783.6
## - STL            1       0.2 11547 -23783.5
## - DET            1       0.3 11547 -23783.5
## - CHI            1       0.3 11547 -23783.5
## - IND            1       0.5 11547 -23782.8
## - HOU            1       0.6 11547 -23782.8
## - WAS            1       0.7 11547 -23782.5
## - GB             1       0.7 11548 -23782.4
## <none>                       11547 -23782.1
## - SEA            1       0.9 11548 -23782.0
## - DEN            1       1.0 11548 -23781.8
## - bad_weather_1  1       1.1 11548 -23781.6
## - grass_1        1       1.3 11548 -23781.1
## - CAR            1       1.3 11548 -23781.1
## - PIT            1       1.3 11548 -23780.9
## - NYJ            1       1.4 11548 -23780.8
## - NOR            1       1.6 11548 -23780.4
## - home_team_1    1       2.3 11549 -23778.6
## - cold_weather   1       5.0 11552 -23772.3
## - avg_rbry_plyr  1    7949.1 19496  -9388.1
## 
## Step:  AIC=-23783.84
## ry ~ cold_weather + home_team_1 + BAL + CAR + CHI + DEN + DET + 
##     GB + HOU + IND + NE + NOR + NYG + NYJ + PHI + PIT + SD + 
##     SEA + STL + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - NE             1       0.1 11547 -23785.6
## - BAL            1       0.2 11547 -23785.4
## - PHI            1       0.2 11547 -23785.4
## - avg_rbry_pos   1       0.2 11547 -23785.4
## - SD             1       0.2 11547 -23785.3
## - NYG            1       0.3 11547 -23785.2
## - CHI            1       0.3 11547 -23785.2
## - STL            1       0.3 11547 -23785.2
## - DET            1       0.3 11547 -23785.1
## - IND            1       0.5 11547 -23784.6
## - HOU            1       0.6 11548 -23784.4
## - GB             1       0.7 11548 -23784.2
## - WAS            1       0.7 11548 -23784.1
## - SEA            1       0.8 11548 -23783.9
## <none>                       11547 -23783.8
## - DEN            1       1.0 11548 -23783.4
## - bad_weather_1  1       1.1 11548 -23783.3
## - grass_1        1       1.2 11548 -23782.9
## - CAR            1       1.2 11548 -23782.9
## - PIT            1       1.3 11548 -23782.7
## - NYJ            1       1.3 11548 -23782.6
## - NOR            1       1.5 11548 -23782.3
## - home_team_1    1       2.3 11549 -23780.3
## - cold_weather   1       4.9 11552 -23774.1
## - avg_rbry_plyr  1    7955.5 19502  -9380.9
## 
## Step:  AIC=-23785.59
## ry ~ cold_weather + home_team_1 + BAL + CAR + CHI + DEN + DET + 
##     GB + HOU + IND + NOR + NYG + NYJ + PHI + PIT + SD + SEA + 
##     STL + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS    AIC
## - BAL            1       0.2 11547 -23787
## - PHI            1       0.2 11547 -23787
## - avg_rbry_pos   1       0.2 11547 -23787
## - SD             1       0.2 11547 -23787
## - CHI            1       0.2 11547 -23787
## - NYG            1       0.3 11547 -23787
## - STL            1       0.3 11547 -23787
## - DET            1       0.3 11547 -23787
## - IND            1       0.5 11547 -23787
## - GB             1       0.6 11548 -23786
## - HOU            1       0.6 11548 -23786
## - WAS            1       0.8 11548 -23786
## - SEA            1       0.8 11548 -23786
## <none>                       11547 -23786
## - bad_weather_1  1       1.1 11548 -23785
## - DEN            1       1.1 11548 -23785
## - grass_1        1       1.1 11548 -23785
## - CAR            1       1.2 11548 -23785
## - PIT            1       1.3 11548 -23785
## - NYJ            1       1.3 11548 -23785
## - NOR            1       1.4 11548 -23784
## - home_team_1    1       2.3 11549 -23782
## - cold_weather   1       4.8 11552 -23776
## - avg_rbry_plyr  1    7956.1 19503  -9382
## 
## Step:  AIC=-23787.19
## ry ~ cold_weather + home_team_1 + CAR + CHI + DEN + DET + GB + 
##     HOU + IND + NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + 
##     WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - PHI            1       0.2 11547 -23788.8
## - SD             1       0.2 11547 -23788.8
## - avg_rbry_pos   1       0.2 11547 -23788.7
## - CHI            1       0.2 11547 -23788.7
## - NYG            1       0.3 11548 -23788.4
## - STL            1       0.3 11548 -23788.4
## - DET            1       0.4 11548 -23788.3
## - IND            1       0.4 11548 -23788.1
## - GB             1       0.6 11548 -23787.8
## - HOU            1       0.7 11548 -23787.5
## - SEA            1       0.7 11548 -23787.4
## - WAS            1       0.8 11548 -23787.3
## <none>                       11547 -23787.2
## - bad_weather_1  1       1.1 11548 -23786.6
## - grass_1        1       1.1 11548 -23786.6
## - DEN            1       1.1 11548 -23786.5
## - CAR            1       1.1 11548 -23786.5
## - PIT            1       1.2 11548 -23786.3
## - NYJ            1       1.2 11548 -23786.3
## - NOR            1       1.4 11548 -23785.9
## - home_team_1    1       2.2 11549 -23783.9
## - cold_weather   1       4.8 11552 -23777.9
## - avg_rbry_plyr  1    7959.8 19507  -9378.4
## 
## Step:  AIC=-23788.83
## ry ~ cold_weather + home_team_1 + CAR + CHI + DEN + DET + GB + 
##     HOU + IND + NOR + NYG + NYJ + PIT + SD + SEA + STL + WAS + 
##     avg_rbry_plyr + avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - SD             1       0.2 11548 -23790.4
## - CHI            1       0.2 11548 -23790.4
## - avg_rbry_pos   1       0.2 11548 -23790.4
## - NYG            1       0.4 11548 -23790.0
## - STL            1       0.4 11548 -23790.0
## - DET            1       0.4 11548 -23789.9
## - IND            1       0.4 11548 -23789.8
## - GB             1       0.6 11548 -23789.5
## - SEA            1       0.7 11548 -23789.2
## - HOU            1       0.7 11548 -23789.1
## <none>                       11547 -23788.8
## - WAS            1       0.9 11548 -23788.8
## - bad_weather_1  1       1.1 11548 -23788.3
## - CAR            1       1.1 11548 -23788.2
## - PIT            1       1.1 11548 -23788.1
## - grass_1        1       1.2 11548 -23788.1
## - NYJ            1       1.2 11548 -23788.0
## - DEN            1       1.2 11548 -23788.0
## - NOR            1       1.3 11549 -23787.6
## - home_team_1    1       2.2 11550 -23785.6
## - cold_weather   1       4.7 11552 -23779.6
## - avg_rbry_plyr  1    7966.8 19514  -9370.4
## 
## Step:  AIC=-23790.43
## ry ~ cold_weather + home_team_1 + CAR + CHI + DEN + DET + GB + 
##     HOU + IND + NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - CHI            1       0.2 11548 -23792.0
## - avg_rbry_pos   1       0.2 11548 -23792.0
## - NYG            1       0.4 11548 -23791.5
## - STL            1       0.4 11548 -23791.5
## - IND            1       0.4 11548 -23791.5
## - DET            1       0.4 11548 -23791.5
## - GB             1       0.5 11548 -23791.2
## - SEA            1       0.7 11548 -23790.8
## - HOU            1       0.8 11548 -23790.6
## <none>                       11548 -23790.4
## - WAS            1       0.9 11548 -23790.3
## - CAR            1       1.0 11548 -23789.9
## - bad_weather_1  1       1.1 11549 -23789.8
## - PIT            1       1.1 11549 -23789.8
## - NYJ            1       1.2 11549 -23789.7
## - DEN            1       1.3 11549 -23789.4
## - grass_1        1       1.3 11549 -23789.4
## - NOR            1       1.3 11549 -23789.3
## - home_team_1    1       2.2 11550 -23787.3
## - cold_weather   1       4.8 11552 -23781.0
## - avg_rbry_plyr  1    7970.7 19518  -9366.6
## 
## Step:  AIC=-23792.02
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU + 
##     IND + NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - avg_rbry_pos   1       0.2 11548 -23793.5
## - IND            1       0.4 11548 -23793.1
## - NYG            1       0.4 11548 -23793.1
## - STL            1       0.4 11548 -23793.1
## - DET            1       0.4 11548 -23793.0
## - GB             1       0.5 11548 -23792.8
## - SEA            1       0.6 11548 -23792.5
## - HOU            1       0.8 11548 -23792.1
## <none>                       11548 -23792.0
## - WAS            1       1.0 11549 -23791.7
## - CAR            1       1.0 11549 -23791.6
## - PIT            1       1.0 11549 -23791.5
## - bad_weather_1  1       1.1 11549 -23791.5
## - NYJ            1       1.1 11549 -23791.4
## - NOR            1       1.3 11549 -23791.0
## - DEN            1       1.3 11549 -23790.9
## - grass_1        1       1.3 11549 -23790.9
## - home_team_1    1       2.2 11550 -23788.9
## - cold_weather   1       4.7 11552 -23782.7
## - avg_rbry_plyr  1    7973.7 19521  -9364.2
## 
## Step:  AIC=-23793.55
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU + 
##     IND + NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - IND            1       0.4 11548 -23794.6
## - STL            1       0.4 11548 -23794.6
## - NYG            1       0.4 11548 -23794.6
## - DET            1       0.4 11548 -23794.5
## - GB             1       0.5 11548 -23794.4
## - SEA            1       0.7 11548 -23794.0
## - HOU            1       0.8 11549 -23793.7
## <none>                       11548 -23793.5
## - WAS            1       1.0 11549 -23793.3
## - CAR            1       1.0 11549 -23793.1
## - PIT            1       1.1 11549 -23793.0
## - bad_weather_1  1       1.1 11549 -23793.0
## - NYJ            1       1.1 11549 -23792.9
## - NOR            1       1.2 11549 -23792.6
## - DEN            1       1.3 11549 -23792.4
## - grass_1        1       1.3 11549 -23792.4
## - home_team_1    1       2.2 11550 -23790.4
## - cold_weather   1       4.7 11553 -23784.3
## - avg_rbry_plyr  1   15898.1 27446     -2.1
## 
## Step:  AIC=-23794.64
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU + 
##     NOR + NYG + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - NYG            1       0.5 11549 -23795.6
## - STL            1       0.5 11549 -23795.6
## - GB             1       0.5 11549 -23795.5
## - DET            1       0.5 11549 -23795.5
## - SEA            1       0.6 11549 -23795.2
## <none>                       11548 -23794.6
## - HOU            1       0.9 11549 -23794.6
## - CAR            1       1.0 11549 -23794.3
## - WAS            1       1.0 11549 -23794.3
## - PIT            1       1.0 11549 -23794.2
## - NYJ            1       1.1 11549 -23794.1
## - bad_weather_1  1       1.1 11549 -23794.1
## - NOR            1       1.1 11549 -23793.9
## - grass_1        1       1.2 11549 -23793.8
## - DEN            1       1.4 11550 -23793.4
## - home_team_1    1       2.3 11551 -23791.1
## - cold_weather   1       4.8 11553 -23785.3
## - avg_rbry_plyr  1   15899.7 27448     -2.1
## 
## Step:  AIC=-23795.56
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU + 
##     NOR + NYJ + PIT + SEA + STL + WAS + avg_rbry_plyr + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - STL            1       0.4 11549 -23796.6
## - DET            1       0.5 11549 -23796.5
## - GB             1       0.5 11549 -23796.3
## - SEA            1       0.7 11549 -23796.0
## - HOU            1       0.8 11550 -23795.6
## <none>                       11549 -23795.6
## - WAS            1       0.9 11550 -23795.3
## - CAR            1       1.0 11550 -23795.1
## - PIT            1       1.1 11550 -23795.0
## - bad_weather_1  1       1.1 11550 -23794.9
## - NYJ            1       1.1 11550 -23794.8
## - NOR            1       1.2 11550 -23794.6
## - DEN            1       1.3 11550 -23794.5
## - grass_1        1       1.4 11550 -23794.3
## - home_team_1    1       2.4 11551 -23791.8
## - cold_weather   1       4.9 11554 -23785.9
## - avg_rbry_plyr  1   15899.7 27448     -3.7
## 
## Step:  AIC=-23796.57
## ry ~ cold_weather + home_team_1 + CAR + DEN + DET + GB + HOU + 
##     NOR + NYJ + PIT + SEA + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - DET            1       0.4 11550 -23797.6
## - GB             1       0.5 11550 -23797.3
## - SEA            1       0.7 11550 -23796.8
## - HOU            1       0.7 11550 -23796.8
## <none>                       11549 -23796.6
## - WAS            1       0.9 11550 -23796.4
## - CAR            1       1.1 11550 -23796.0
## - bad_weather_1  1       1.1 11550 -23796.0
## - PIT            1       1.1 11550 -23795.9
## - NYJ            1       1.2 11550 -23795.7
## - DEN            1       1.3 11550 -23795.6
## - NOR            1       1.3 11550 -23795.4
## - grass_1        1       1.5 11551 -23795.1
## - home_team_1    1       2.3 11551 -23793.2
## - cold_weather   1       4.8 11554 -23787.0
## - avg_rbry_plyr  1   15901.8 27451     -3.1
## 
## Step:  AIC=-23797.61
## ry ~ cold_weather + home_team_1 + CAR + DEN + GB + HOU + NOR + 
##     NYJ + PIT + SEA + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS    AIC
## - GB             1       0.6 11550 -23798
## - HOU            1       0.7 11550 -23798
## - SEA            1       0.8 11550 -23798
## <none>                       11550 -23798
## - WAS            1       0.9 11550 -23798
## - bad_weather_1  1       1.1 11551 -23797
## - CAR            1       1.1 11551 -23797
## - PIT            1       1.2 11551 -23797
## - DEN            1       1.2 11551 -23797
## - NYJ            1       1.3 11551 -23797
## - NOR            1       1.4 11551 -23796
## - grass_1        1       1.6 11551 -23796
## - home_team_1    1       2.2 11552 -23795
## - cold_weather   1       4.7 11554 -23788
## - avg_rbry_plyr  1   15902.5 27452     -4
## 
## Step:  AIC=-23798.23
## ry ~ cold_weather + home_team_1 + CAR + DEN + HOU + NOR + NYJ + 
##     PIT + SEA + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - SEA            1       0.7 11551 -23798.5
## - HOU            1       0.7 11551 -23798.5
## <none>                       11550 -23798.2
## - WAS            1       0.9 11551 -23798.0
## - CAR            1       1.1 11551 -23797.7
## - bad_weather_1  1       1.1 11551 -23797.7
## - PIT            1       1.1 11551 -23797.7
## - NYJ            1       1.2 11551 -23797.3
## - DEN            1       1.3 11551 -23797.1
## - NOR            1       1.4 11551 -23797.0
## - grass_1        1       1.7 11552 -23796.1
## - home_team_1    1       2.1 11552 -23795.2
## - cold_weather   1       4.5 11555 -23789.5
## - avg_rbry_plyr  1   15902.0 27452     -5.9
## 
## Step:  AIC=-23798.52
## ry ~ cold_weather + home_team_1 + CAR + DEN + HOU + NOR + NYJ + 
##     PIT + WAS + avg_rbry_plyr + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS      AIC
## - HOU            1       0.8 11552 -23798.6
## <none>                       11551 -23798.5
## - CAR            1       1.0 11552 -23798.1
## - PIT            1       1.0 11552 -23798.1
## - WAS            1       1.0 11552 -23798.1
## - bad_weather_1  1       1.0 11552 -23798.0
## - NYJ            1       1.1 11552 -23797.9
## - NOR            1       1.3 11552 -23797.5
## - DEN            1       1.4 11552 -23797.2
## - grass_1        1       1.5 11552 -23796.9
## - home_team_1    1       2.0 11553 -23795.8
## - cold_weather   1       4.3 11555 -23790.3
## - avg_rbry_plyr  1   15903.5 27454     -5.7
## 
## Step:  AIC=-23798.65
## ry ~ cold_weather + home_team_1 + CAR + DEN + NOR + NYJ + PIT + 
##     WAS + avg_rbry_plyr + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq   RSS    AIC
## <none>                       11552 -23799
## - WAS            1       1.0 11552 -23798
## - PIT            1       1.0 11553 -23798
## - CAR            1       1.1 11553 -23798
## - bad_weather_1  1       1.1 11553 -23798
## - NYJ            1       1.2 11553 -23798
## - DEN            1       1.3 11553 -23798
## - NOR            1       1.4 11553 -23797
## - grass_1        1       1.6 11553 -23797
## - home_team_1    1       1.8 11553 -23797
## - cold_weather   1       4.2 11556 -23791
## - avg_rbry_plyr  1   15904.5 27456     -6

Rushing attempts

PreProcess:

set.seed(123)
splitra <- sample.split(nfl_data$ra, SplitRatio = 0.7)
Trainra <- subset(nfl_data, split == TRUE)
Testra <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainra, method = c("center", "scale"))
trainTransformedra <- predict(preProcValues, Trainra)
testTransformedra <- predict(preProcValues, Testra)

ggpairs:

ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("ra",colnames(filtered_nfl_data_fields[46:51]))])

raregform <- formula(paste("ra ~ ", 
                           paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegRushAtt <- lm(raregform, data = trainTransformedra)
summary(linRegRushAtt)
## 
## Call:
## lm(formula = raregform, data = trainTransformedra)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8046 -0.0854 -0.0090  0.0496  5.3831 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      8.104e-15  3.326e-03   0.000 1.000000    
## height          -2.162e-03  6.453e-03  -0.335 0.737573    
## weight          -1.279e-03  6.048e-03  -0.212 0.832493    
## cold_weather     1.184e-02  3.501e-03   3.381 0.000724 ***
## hot_weather     -3.506e-03  3.356e-03  -1.045 0.296176    
## home_team_1      5.312e-03  3.619e-03   1.468 0.142168    
## forty1           2.705e-02  5.740e-03   4.712 2.46e-06 ***
## vertical1        2.959e-04  4.413e-03   0.067 0.946539    
## ARI              7.646e-03  4.653e-03   1.643 0.100312    
## ATL              6.424e-03  4.675e-03   1.374 0.169437    
## BAL              7.016e-03  4.679e-03   1.499 0.133760    
## BUF             -8.683e-04  4.619e-03  -0.188 0.850888    
## CAR             -2.889e-03  4.589e-03  -0.630 0.528932    
## CHI              2.194e-03  4.537e-03   0.483 0.628766    
## CIN              9.587e-03  4.621e-03   2.075 0.038017 *  
## CLE              9.419e-03  4.600e-03   2.048 0.040589 *  
## DAL              2.418e-03  4.646e-03   0.521 0.602708    
## DEN              1.599e-02  4.664e-03   3.429 0.000607 ***
## DET              1.059e-02  4.600e-03   2.302 0.021340 *  
## GB               5.605e-04  4.735e-03   0.118 0.905783    
## HOU              1.138e-02  4.679e-03   2.432 0.015023 *  
## IND              2.856e-03  4.645e-03   0.615 0.538603    
## JAC              2.146e-03  4.531e-03   0.474 0.635752    
## KC              -3.085e-03  4.630e-03  -0.666 0.505194    
## MIA              3.608e-03  4.556e-03   0.792 0.428412    
## MINN            -6.259e-03  4.584e-03  -1.365 0.172130    
## NE               6.544e-03  4.787e-03   1.367 0.171597    
## NOR             -1.954e-03  4.772e-03  -0.409 0.682181    
## NYG              1.218e-02  4.665e-03   2.611 0.009035 ** 
## NYJ             -2.709e-03  4.647e-03  -0.583 0.560015    
## OAK              2.270e-03  4.677e-03   0.485 0.627353    
## PHI             -4.940e-03  4.532e-03  -1.090 0.275639    
## PIT              1.039e-03  4.651e-03   0.223 0.823167    
## SD               8.241e-03  4.564e-03   1.806 0.070952 .  
## SEA             -2.708e-03  4.736e-03  -0.572 0.567490    
## STL              1.129e-02  4.610e-03   2.449 0.014334 *  
## TB               5.189e-03  4.567e-03   1.136 0.255896    
## TEN              6.032e-03  4.594e-03   1.313 0.189196    
## WAS              7.307e-03  4.619e-03   1.582 0.113631    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -1.540e-03  4.247e-03  -0.363 0.716951    
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr    7.971e-01  5.083e-03 156.823  < 2e-16 ***
## avg_rbry_pos     5.532e-02  5.922e-03   9.341  < 2e-16 ***
## avg_fuml_plyr    1.334e-03  4.913e-03   0.271 0.786013    
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -3.404e-03  5.337e-03  -0.638 0.523639    
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -3.779e-03  3.827e-03  -0.987 0.323445    
## bad_weather_1    2.234e-03  3.383e-03   0.660 0.509067    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5514 on 27438 degrees of freedom
## Multiple R-squared:  0.6965, Adjusted R-squared:  0.696 
## F-statistic:  1399 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegRushAtt2 <- update(linRegRushYd,~.-height-weight-hot_weather-home_team_1-age-is_TE
                         -vertical1-ARI-ATL-BAL - BUF - CAR - CHI
                         -CIN - CLE - DAL - GB - IND - JAC - KC - MIA 
                         -MINN - NE - NOR -NYJ - OAK - PHI - PIT -SD - SEA 
                         -TB - TEN - WAS
                         -avg_rectd_plyr-avg_trg_team-avg_tdr_team-avg_rbra_team
                         -avg_fuml_team-avg_fuml_plyr-avg_qbints_team-avg_qbtdp_team-avg_qbints_plyr
                         -bad_weather_1-grass_1)

summary(linRegRushAtt2)
## 
## Call:
## lm(formula = ry ~ cold_weather + forty1 + DEN + DET + HOU + NYG + 
##     STL + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr, data = trainTransformedry)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4811 -0.0751 -0.0163  0.0151  7.1750 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.336e-14  3.912e-03   0.000 1.000000    
## cold_weather    1.442e-02  3.938e-03   3.662 0.000251 ***
## forty1         -1.982e-04  4.525e-03  -0.044 0.965059    
## DEN             7.910e-03  3.924e-03   2.016 0.043855 *  
## DET             4.997e-03  3.933e-03   1.271 0.203905    
## HOU             6.066e-03  3.935e-03   1.541 0.123208    
## NYG             6.172e-03  3.929e-03   1.571 0.116167    
## STL             4.426e-03  3.928e-03   1.127 0.259865    
## avg_rbry_plyr   7.584e-01  5.588e-03 135.723  < 2e-16 ***
## avg_rbry_pos    4.004e-03  5.521e-03   0.725 0.468327    
## avg_qbtdp_plyr -1.094e-03  4.459e-03  -0.245 0.806247    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6486 on 27473 degrees of freedom
## Multiple R-squared:  0.5795, Adjusted R-squared:  0.5793 
## F-statistic:  3786 on 10 and 27473 DF,  p-value: < 2.2e-16
linRegRushAtt3 <- update(linRegRushYd,~.-is_WR-forty1-is_TE-DET-HOU-NYG-STL-avg_rbry_pos)
summary(linRegRushAtt3)
## 
## Call:
## lm(formula = ry ~ height + weight + cold_weather + hot_weather + 
##     home_team_1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + GB + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYJ + OAK + PHI + PIT + SD + SEA + TB + TEN + 
##     WAS + avg_trg_team + avg_rectd_plyr + avg_tdr_team + avg_rbra_team + 
##     avg_rbry_plyr + avg_fuml_plyr + avg_fuml_team + avg_qbints_team + 
##     avg_qbtdp_plyr + avg_qbtdp_team + grass_1 + bad_weather_1, 
##     data = trainTransformedry)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4896 -0.0836 -0.0125  0.0242  7.1660 
## 
## Coefficients: (2 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      2.344e-14  3.913e-03   0.000 1.000000    
## height          -4.250e-03  6.636e-03  -0.641 0.521852    
## weight           2.594e-03  5.973e-03   0.434 0.664046    
## cold_weather     1.399e-02  4.119e-03   3.396 0.000685 ***
## hot_weather     -1.398e-03  3.948e-03  -0.354 0.723326    
## home_team_1      1.004e-02  4.257e-03   2.357 0.018410 *  
## vertical1       -1.282e-03  4.435e-03  -0.289 0.772558    
## ARI              1.483e-03  1.001e-02   0.148 0.882240    
## ATL              1.719e-03  1.975e-02   0.087 0.930629    
## BAL             -4.354e-03  1.319e-02  -0.330 0.741352    
## BUF             -3.768e-03  9.869e-03  -0.382 0.702625    
## CAR             -5.674e-03  7.359e-03  -0.771 0.440718    
## CHI             -8.120e-03  9.801e-03  -0.828 0.407412    
## CIN             -4.125e-03  7.453e-03  -0.553 0.579998    
## CLE             -1.419e-03  5.366e-03  -0.265 0.791380    
## DAL             -1.644e-03  5.768e-03  -0.285 0.775585    
## DEN              1.147e-04  2.093e-02   0.005 0.995629    
## GB              -6.551e-03  8.796e-03  -0.745 0.456438    
## IND             -9.439e-03  4.924e-03  -1.917 0.055243 .  
## JAC             -8.556e-03  8.212e-03  -1.042 0.297482    
## KC              -6.296e-04  5.422e-03  -0.116 0.907560    
## MIA             -1.145e-03  5.612e-03  -0.204 0.838315    
## MINN             1.818e-03  1.202e-02   0.151 0.879798    
## NE               3.165e-03  3.194e-02   0.099 0.921068    
## NOR             -4.459e-03  2.444e-02  -0.182 0.855199    
## NYJ             -1.296e-02  1.418e-02  -0.914 0.360618    
## OAK              1.173e-03  1.366e-02   0.086 0.931562    
## PHI             -4.167e-03  1.563e-02  -0.267 0.789842    
## PIT             -9.834e-03  5.091e-03  -1.932 0.053398 .  
## SD              -1.064e-02  1.536e-02  -0.693 0.488426    
## SEA             -3.444e-03  1.131e-02  -0.305 0.760741    
## TB              -5.047e-03  1.117e-02  -0.452 0.651391    
## TEN              1.429e-03  6.043e-03   0.236 0.813091    
## WAS              6.074e-03  6.196e-03   0.980 0.326982    
## avg_trg_team     7.333e-03  8.678e-03   0.845 0.398129    
## avg_rectd_plyr   1.483e-03  4.720e-03   0.314 0.753296    
## avg_tdr_team    -2.054e-02  3.991e-02  -0.515 0.606745    
## avg_rbra_team    1.626e-02  4.065e-02   0.400 0.689110    
## avg_rbry_plyr    7.604e-01  4.902e-03 155.133  < 2e-16 ***
## avg_fuml_plyr    7.528e-04  5.779e-03   0.130 0.896352    
## avg_fuml_team    4.848e-03  4.544e-02   0.107 0.915024    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -3.021e-04  6.019e-03  -0.050 0.959977    
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -7.836e-03  4.502e-03  -1.741 0.081769 .  
## bad_weather_1    6.398e-03  3.980e-03   1.607 0.107989    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6487 on 27440 degrees of freedom
## Multiple R-squared:  0.5799, Adjusted R-squared:  0.5792 
## F-statistic: 880.8 on 43 and 27440 DF,  p-value: < 2.2e-16

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

RushattPredicted <- predict(linRegRushAtt, newdata = testTransformedra)
## Warning in predict.lm(linRegRushAtt, newdata = testTransformedra):
## prediction from a rank-deficient fit may be misleading
SSEruatt <- sum((RushattPredicted - testTransformedra$ra)^2)
SSTruatt <- sum((mean(nfl_data$ra)-testTransformedra$ra)^2)
r2_ruatt <- 1 - SSEruatt/SSTruatt 
r2_ruatt
## [1] 0.958404
rmse_ruatt <- sqrt(SSEruatt/nrow(testTransformedra))
rmse_ruatt
## [1] 0.5583721

Regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegRushAtt3, which = c(1:3,2))

Summary statistics:

confint(linRegRushAtt3)
##                        2.5 %       97.5 %
## (Intercept)     -0.007669245 0.0076692451
## height          -0.017256818 0.0087562940
## weight          -0.009113117 0.0143017475
## cold_weather     0.005913936 0.0220595475
## hot_weather     -0.009137059 0.0063413757
## home_team_1      0.001691644 0.0183806622
## vertical1       -0.009974415 0.0074107595
## ARI             -0.018134356 0.0210994601
## ATL             -0.036992629 0.0404313835
## BAL             -0.030210343 0.0215021045
## BUF             -0.023112326 0.0155764292
## CAR             -0.020098113 0.0087504440
## CHI             -0.027330666 0.0110907770
## CIN             -0.018733519 0.0104842673
## CLE             -0.011937414 0.0090984867
## DAL             -0.012949042 0.0096605859
## DEN             -0.040914291 0.0411436294
## GB              -0.023792568 0.0106904874
## IND             -0.019089129 0.0002117549
## JAC             -0.024651979 0.0075401749
## KC              -0.011257522 0.0099982754
## MIA             -0.012145205 0.0098548783
## MINN            -0.021742134 0.0253776222
## NE              -0.059432674 0.0657618248
## NOR             -0.052353695 0.0434352291
## NYJ             -0.040754676 0.0148292770
## OAK             -0.025602975 0.0279494003
## PHI             -0.034808261 0.0264752052
## PIT             -0.019811999 0.0001439443
## SD              -0.040745213 0.0194631912
## SEA             -0.025611367 0.0187235469
## TB              -0.026939122 0.0168457355
## TEN             -0.010416503 0.0132743474
## WAS             -0.006071133 0.0182184220
## avg_trg_team    -0.009676353 0.0243414921
## avg_rectd_plyr  -0.007767648 0.0107345278
## avg_tdr_team    -0.098773936 0.0576858279
## avg_rbra_team   -0.063405957 0.0959277180
## avg_rbry_plyr    0.750805188 0.7700203321
## avg_fuml_plyr   -0.010573740 0.0120793526
## avg_fuml_team   -0.084210860 0.0939076059
## avg_qbints_team           NA           NA
## avg_qbtdp_plyr  -0.012100583 0.0114964322
## avg_qbtdp_team            NA           NA
## grass_1         -0.016659292 0.0009880277
## bad_weather_1   -0.001403838 0.0141992619
coef(summary(linRegRushAtt3))
##                     Estimate  Std. Error       t value     Pr(>|t|)
## (Intercept)     2.344479e-14 0.003912779  5.991850e-12 1.0000000000
## height         -4.250262e-03 0.006635827 -6.405022e-01 0.5218515088
## weight          2.594315e-03 0.005973026  4.343385e-01 0.6640460685
## cold_weather    1.398674e-02 0.004118672  3.395935e+00 0.0006849163
## hot_weather    -1.397841e-03 0.003948479 -3.540203e-01 0.7233264149
## home_team_1     1.003615e-02 0.004257293  2.357403e+00 0.0184102659
## vertical1      -1.281828e-03 0.004434879 -2.890333e-01 0.7725580582
## ARI             1.482552e-03 0.010008369  1.481312e-01 0.8822402932
## ATL             1.719377e-03 0.019750515  8.705481e-02 0.9306285825
## BAL            -4.354119e-03 0.013191611 -3.300673e-01 0.7413516436
## BUF            -3.767948e-03 0.009869326 -3.817837e-01 0.7026247322
## CAR            -5.673834e-03 0.007359136 -7.709919e-01 0.4407183832
## CHI            -8.119944e-03 0.009801136 -8.284697e-01 0.4074117522
## CIN            -4.124626e-03 0.007453325 -5.533941e-01 0.5799981114
## CLE            -1.419464e-03 0.005366163 -2.645211e-01 0.7913803617
## DAL            -1.644228e-03 0.005767614 -2.850794e-01 0.7755854311
## DEN             1.146694e-04 0.020932604  5.478027e-03 0.9956292289
## GB             -6.551040e-03 0.008796471 -7.447350e-01 0.4564383012
## IND            -9.438687e-03 0.004923568 -1.917042e+00 0.0552429659
## JAC            -8.555902e-03 0.008212073 -1.041869e+00 0.2974817178
## KC             -6.296235e-04 0.005422258 -1.161183e-01 0.9075596145
## MIA            -1.145164e-03 0.005612122 -2.040518e-01 0.8383145395
## MINN            1.817744e-03 0.012020037  1.512262e-01 0.8797984050
## NE              3.164575e-03 0.031936550  9.908945e-02 0.9210679708
## NOR            -4.459233e-03 0.024435321 -1.824913e-01 0.8551985469
## NYJ            -1.296270e-02 0.014179215 -9.142043e-01 0.3606175306
## OAK             1.173213e-03 0.013660969  8.588063e-02 0.9315619327
## PHI            -4.166528e-03 0.015633135 -2.665190e-01 0.7898415213
## PIT            -9.834027e-03 0.005090671 -1.931774e+00 0.0533976464
## SD             -1.064101e-02 0.015358891 -6.928241e-01 0.4884257835
## SEA            -3.443910e-03 0.011309636 -3.045111e-01 0.7607408121
## TB             -5.046693e-03 0.011169319 -4.518354e-01 0.6513911628
## TEN             1.428922e-03 0.006043429  2.364423e-01 0.8130912061
## WAS             6.073644e-03 0.006196156  9.802279e-01 0.3269822992
## avg_trg_team    7.332570e-03 0.008677798  8.449804e-01 0.3981291504
## avg_rectd_plyr  1.483440e-03 0.004719821  3.143000e-01 0.7532955779
## avg_tdr_team   -2.054405e-02 0.039912178 -5.147315e-01 0.6067448256
## avg_rbra_team   1.626088e-02 0.040645300  4.000679e-01 0.6891096097
## avg_rbry_plyr   7.604128e-01 0.004901696  1.551326e+02 0.0000000000
## avg_fuml_plyr   7.528063e-04 0.005778701  1.302726e-01 0.8963517388
## avg_fuml_team   4.848373e-03 0.045437215  1.067049e-01 0.9150238822
## avg_qbtdp_plyr -3.020756e-04 0.006019492 -5.018291e-02 0.9599769975
## grass_1        -7.835632e-03 0.004501752 -1.740574e+00 0.0817694614
## bad_weather_1   6.397712e-03 0.003980280  1.607352e+00 0.1079886565
anova(linRegRushAtt3)
## Analysis of Variance Table
## 
## Response: ry
##                   Df  Sum Sq Mean Sq    F value    Pr(>F)    
## height             1  1821.4  1821.4  4328.6020 < 2.2e-16 ***
## weight             1  1093.9  1093.9  2599.6901 < 2.2e-16 ***
## cold_weather       1     4.0     4.0     9.5199 0.0020345 ** 
## hot_weather        1     0.3     0.3     0.6398 0.4238057    
## home_team_1        1     3.1     3.1     7.4732 0.0062663 ** 
## vertical1          1    21.9    21.9    52.1045 5.399e-13 ***
## ARI                1     1.0     1.0     2.3860 0.1224362    
## ATL                1     5.3     5.3    12.6629 0.0003736 ***
## BAL                1     5.7     5.7    13.5172 0.0002368 ***
## BUF                1     7.3     7.3    17.2903 3.218e-05 ***
## CAR                1     0.1     0.1     0.2082 0.6481658    
## CHI                1     9.0     9.0    21.4681 3.614e-06 ***
## CIN                1     3.6     3.6     8.4879 0.0035780 ** 
## CLE                1     1.9     1.9     4.4084 0.0357708 *  
## DAL                1     3.7     3.7     8.8898 0.0028702 ** 
## DEN                1     0.1     0.1     0.1739 0.6766667    
## GB                 1     0.7     0.7     1.7186 0.1898847    
## IND                1     4.6     4.6    10.8507 0.0009888 ***
## JAC                1     2.7     2.7     6.4831 0.0108958 *  
## KC                 1     1.5     1.5     3.5452 0.0597286 .  
## MIA                1     0.6     0.6     1.4867 0.2227429    
## MINN               1    17.0    17.0    40.3101 2.201e-10 ***
## NE                 1     3.0     3.0     7.2446 0.0071156 ** 
## NOR                1     6.0     6.0    14.3043 0.0001558 ***
## NYJ                1     2.5     2.5     5.9654 0.0145955 *  
## OAK                1     1.6     1.6     3.7620 0.0524391 .  
## PHI                1     3.0     3.0     7.0162 0.0080823 ** 
## PIT                1     0.0     0.0     0.0095 0.9222679    
## SD                 1     0.0     0.0     0.1015 0.7500854    
## SEA                1     0.2     0.2     0.4016 0.5262656    
## TB                 1     0.1     0.1     0.2326 0.6296331    
## TEN                1     0.0     0.0     0.0004 0.9842026    
## WAS                1     5.7     5.7    13.6255 0.0002236 ***
## avg_trg_team       1     0.6     0.6     1.4230 0.2329197    
## avg_rectd_plyr     1   590.5   590.5  1403.2578 < 2.2e-16 ***
## avg_tdr_team       1     8.7     8.7    20.5736 5.762e-06 ***
## avg_rbra_team      1     0.6     0.6     1.4897 0.2222670    
## avg_rbry_plyr      1 12302.7 12302.7 29238.2353 < 2.2e-16 ***
## avg_fuml_plyr      1     0.0     0.0     0.0148 0.9032697    
## avg_fuml_team      1     0.0     0.0     0.0524 0.8188814    
## avg_qbtdp_plyr     1     0.0     0.0     0.0037 0.9517883    
## grass_1            1     1.2     1.2     2.8654 0.0905158 .  
## bad_weather_1      1     1.1     1.1     2.5836 0.1079887    
## Residuals      27440 11546.1     0.4                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC

aic_ra <- step(lm(raregform, data = trainTransformedra), direction = "backward")
## Start:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - vertical1       1       0.0  8342.3 -32678
## - GB              1       0.0  8342.3 -32678
## - BUF             1       0.0  8342.3 -32678
## - weight          1       0.0  8342.3 -32678
## - PIT             1       0.0  8342.3 -32678
## - avg_fuml_plyr   1       0.0  8342.3 -32678
## - height          1       0.0  8342.3 -32678
## - avg_rectd_plyr  1       0.0  8342.3 -32678
## - NOR             1       0.1  8342.4 -32678
## - JAC             1       0.1  8342.4 -32678
## - CHI             1       0.1  8342.4 -32678
## - OAK             1       0.1  8342.4 -32678
## - DAL             1       0.1  8342.4 -32678
## - SEA             1       0.1  8342.4 -32678
## - NYJ             1       0.1  8342.4 -32678
## - IND             1       0.1  8342.4 -32678
## - CAR             1       0.1  8342.4 -32678
## - avg_qbtdp_plyr  1       0.1  8342.4 -32678
## - bad_weather_1   1       0.1  8342.4 -32678
## - KC              1       0.1  8342.4 -32678
## - MIA             1       0.2  8342.5 -32678
## - grass_1         1       0.3  8342.6 -32677
## - hot_weather     1       0.3  8342.6 -32677
## - PHI             1       0.4  8342.7 -32677
## - TB              1       0.4  8342.7 -32677
## - TEN             1       0.5  8342.8 -32676
## - MINN            1       0.6  8342.9 -32676
## - NE              1       0.6  8342.9 -32676
## - ATL             1       0.6  8342.9 -32676
## <none>                         8342.3 -32676
## - home_team_1     1       0.7  8343.0 -32676
## - BAL             1       0.7  8343.0 -32676
## - WAS             1       0.8  8343.1 -32676
## - ARI             1       0.8  8343.1 -32675
## - SD              1       1.0  8343.3 -32675
## - CLE             1       1.3  8343.6 -32674
## - CIN             1       1.3  8343.6 -32674
## - DET             1       1.6  8343.9 -32673
## - HOU             1       1.8  8344.1 -32672
## - STL             1       1.8  8344.1 -32672
## - NYG             1       2.1  8344.4 -32671
## - cold_weather    1       3.5  8345.8 -32667
## - DEN             1       3.6  8345.9 -32666
## - forty1          1       6.8  8349.1 -32656
## - avg_rbry_pos    1      26.5  8368.8 -32591
## - avg_rbry_plyr   1    7477.5 15819.8 -15091
## 
## Step:  AIC=-32678.18
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - GB              1       0.0  8342.3 -32680
## - BUF             1       0.0  8342.3 -32680
## - weight          1       0.0  8342.3 -32680
## - PIT             1       0.0  8342.3 -32680
## - avg_fuml_plyr   1       0.0  8342.3 -32680
## - height          1       0.0  8342.3 -32680
## - avg_rectd_plyr  1       0.0  8342.3 -32680
## - NOR             1       0.1  8342.4 -32680
## - JAC             1       0.1  8342.4 -32680
## - CHI             1       0.1  8342.4 -32680
## - OAK             1       0.1  8342.4 -32680
## - DAL             1       0.1  8342.4 -32680
## - SEA             1       0.1  8342.4 -32680
## - NYJ             1       0.1  8342.4 -32680
## - IND             1       0.1  8342.4 -32680
## - CAR             1       0.1  8342.4 -32680
## - avg_qbtdp_plyr  1       0.1  8342.4 -32680
## - bad_weather_1   1       0.1  8342.4 -32680
## - KC              1       0.1  8342.4 -32680
## - MIA             1       0.2  8342.5 -32680
## - grass_1         1       0.3  8342.6 -32679
## - hot_weather     1       0.3  8342.6 -32679
## - PHI             1       0.4  8342.7 -32679
## - TB              1       0.4  8342.7 -32679
## - TEN             1       0.5  8342.8 -32678
## - MINN            1       0.6  8342.9 -32678
## - NE              1       0.6  8342.9 -32678
## - ATL             1       0.6  8342.9 -32678
## <none>                         8342.3 -32678
## - home_team_1     1       0.7  8343.0 -32678
## - BAL             1       0.7  8343.0 -32678
## - WAS             1       0.8  8343.1 -32678
## - ARI             1       0.8  8343.1 -32677
## - SD              1       1.0  8343.3 -32677
## - CLE             1       1.3  8343.6 -32676
## - CIN             1       1.3  8343.6 -32676
## - DET             1       1.6  8343.9 -32675
## - HOU             1       1.8  8344.1 -32674
## - STL             1       1.8  8344.1 -32674
## - NYG             1       2.1  8344.4 -32673
## - cold_weather    1       3.5  8345.8 -32669
## - DEN             1       3.6  8345.9 -32668
## - forty1          1       9.1  8351.4 -32650
## - avg_rbry_pos    1      26.5  8368.8 -32593
## - avg_rbry_plyr   1    7498.1 15840.4 -15057
## 
## Step:  AIC=-32680.17
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - PIT             1       0.0  8342.3 -32682
## - weight          1       0.0  8342.3 -32682
## - avg_fuml_plyr   1       0.0  8342.3 -32682
## - BUF             1       0.0  8342.3 -32682
## - height          1       0.0  8342.3 -32682
## - avg_rectd_plyr  1       0.0  8342.4 -32682
## - JAC             1       0.1  8342.4 -32682
## - CHI             1       0.1  8342.4 -32682
## - OAK             1       0.1  8342.4 -32682
## - DAL             1       0.1  8342.4 -32682
## - NOR             1       0.1  8342.4 -32682
## - avg_qbtdp_plyr  1       0.1  8342.4 -32682
## - IND             1       0.1  8342.4 -32682
## - bad_weather_1   1       0.1  8342.4 -32682
## - SEA             1       0.2  8342.5 -32682
## - NYJ             1       0.2  8342.5 -32682
## - CAR             1       0.2  8342.5 -32682
## - KC              1       0.2  8342.5 -32681
## - MIA             1       0.2  8342.5 -32681
## - grass_1         1       0.3  8342.6 -32681
## - hot_weather     1       0.3  8342.6 -32681
## - TB              1       0.5  8342.8 -32681
## - PHI             1       0.5  8342.8 -32680
## <none>                         8342.3 -32680
## - TEN             1       0.6  8342.9 -32680
## - home_team_1     1       0.7  8343.0 -32680
## - ATL             1       0.7  8343.0 -32680
## - NE              1       0.7  8343.0 -32680
## - MINN            1       0.8  8343.1 -32680
## - BAL             1       0.8  8343.2 -32679
## - WAS             1       0.9  8343.3 -32679
## - ARI             1       1.0  8343.3 -32679
## - SD              1       1.2  8343.5 -32678
## - CLE             1       1.6  8343.9 -32677
## - CIN             1       1.6  8344.0 -32677
## - DET             1       2.0  8344.3 -32676
## - HOU             1       2.3  8344.6 -32675
## - STL             1       2.3  8344.6 -32675
## - NYG             1       2.7  8345.0 -32673
## - cold_weather    1       3.5  8345.8 -32671
## - DEN             1       4.7  8347.0 -32667
## - forty1          1       9.1  8351.4 -32652
## - avg_rbry_pos    1      26.6  8368.9 -32595
## - avg_rbry_plyr   1    7498.1 15840.4 -15059
## 
## Step:  AIC=-32682.13
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - weight          1       0.0  8342.3 -32684
## - avg_fuml_plyr   1       0.0  8342.3 -32684
## - height          1       0.0  8342.4 -32684
## - avg_rectd_plyr  1       0.0  8342.4 -32684
## - BUF             1       0.0  8342.4 -32684
## - JAC             1       0.1  8342.4 -32684
## - CHI             1       0.1  8342.4 -32684
## - OAK             1       0.1  8342.4 -32684
## - DAL             1       0.1  8342.4 -32684
## - IND             1       0.1  8342.4 -32684
## - avg_qbtdp_plyr  1       0.1  8342.4 -32684
## - NOR             1       0.1  8342.4 -32684
## - bad_weather_1   1       0.1  8342.5 -32684
## - MIA             1       0.2  8342.5 -32683
## - SEA             1       0.2  8342.5 -32683
## - NYJ             1       0.2  8342.5 -32683
## - CAR             1       0.2  8342.6 -32683
## - KC              1       0.3  8342.6 -32683
## - grass_1         1       0.3  8342.6 -32683
## - hot_weather     1       0.3  8342.7 -32683
## - TB              1       0.5  8342.8 -32683
## <none>                         8342.3 -32682
## - PHI             1       0.6  8343.0 -32682
## - TEN             1       0.7  8343.0 -32682
## - home_team_1     1       0.7  8343.0 -32682
## - ATL             1       0.7  8343.0 -32682
## - NE              1       0.7  8343.0 -32682
## - BAL             1       0.9  8343.2 -32681
## - MINN            1       1.0  8343.3 -32681
## - WAS             1       1.0  8343.3 -32681
## - ARI             1       1.0  8343.4 -32681
## - SD              1       1.3  8343.6 -32680
## - CLE             1       1.7  8344.0 -32679
## - CIN             1       1.7  8344.1 -32678
## - DET             1       2.1  8344.5 -32677
## - HOU             1       2.4  8344.7 -32676
## - STL             1       2.4  8344.7 -32676
## - NYG             1       2.8  8345.2 -32675
## - cold_weather    1       3.6  8345.9 -32672
## - DEN             1       5.1  8347.4 -32667
## - forty1          1       9.1  8351.4 -32654
## - avg_rbry_pos    1      26.6  8368.9 -32597
## - avg_rbry_plyr   1    7500.2 15842.6 -15057
## 
## Step:  AIC=-32684.09
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - avg_fuml_plyr   1       0.0  8342.4 -32686
## - BUF             1       0.0  8342.4 -32686
## - avg_rectd_plyr  1       0.0  8342.4 -32686
## - JAC             1       0.1  8342.4 -32686
## - CHI             1       0.1  8342.4 -32686
## - OAK             1       0.1  8342.4 -32686
## - DAL             1       0.1  8342.4 -32686
## - avg_qbtdp_plyr  1       0.1  8342.4 -32686
## - IND             1       0.1  8342.5 -32686
## - NOR             1       0.1  8342.5 -32686
## - bad_weather_1   1       0.1  8342.5 -32686
## - height          1       0.1  8342.5 -32686
## - MIA             1       0.2  8342.5 -32685
## - NYJ             1       0.2  8342.6 -32685
## - SEA             1       0.2  8342.6 -32685
## - CAR             1       0.3  8342.6 -32685
## - KC              1       0.3  8342.6 -32685
## - grass_1         1       0.3  8342.6 -32685
## - hot_weather     1       0.3  8342.7 -32685
## - TB              1       0.5  8342.8 -32685
## <none>                         8342.3 -32684
## - PHI             1       0.6  8343.0 -32684
## - home_team_1     1       0.7  8343.0 -32684
## - TEN             1       0.7  8343.0 -32684
## - ATL             1       0.7  8343.1 -32684
## - NE              1       0.7  8343.1 -32684
## - BAL             1       0.9  8343.2 -32683
## - MINN            1       1.0  8343.3 -32683
## - WAS             1       1.0  8343.3 -32683
## - ARI             1       1.0  8343.4 -32683
## - SD              1       1.3  8343.6 -32682
## - CLE             1       1.7  8344.0 -32680
## - CIN             1       1.8  8344.1 -32680
## - DET             1       2.1  8344.5 -32679
## - STL             1       2.4  8344.8 -32678
## - HOU             1       2.4  8344.8 -32678
## - NYG             1       2.9  8345.2 -32677
## - cold_weather    1       3.6  8345.9 -32674
## - DEN             1       5.1  8347.4 -32669
## - forty1          1      10.8  8353.2 -32650
## - avg_rbry_pos    1      30.3  8372.7 -32586
## - avg_rbry_plyr   1    7517.1 15859.5 -15030
## 
## Step:  AIC=-32686
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BUF             1       0.0  8342.4 -32688
## - avg_rectd_plyr  1       0.0  8342.4 -32688
## - JAC             1       0.1  8342.4 -32688
## - OAK             1       0.1  8342.4 -32688
## - CHI             1       0.1  8342.4 -32688
## - DAL             1       0.1  8342.4 -32688
## - avg_qbtdp_plyr  1       0.1  8342.5 -32688
## - IND             1       0.1  8342.5 -32688
## - NOR             1       0.1  8342.5 -32688
## - bad_weather_1   1       0.1  8342.5 -32688
## - height          1       0.1  8342.5 -32688
## - NYJ             1       0.2  8342.6 -32687
## - MIA             1       0.2  8342.6 -32687
## - SEA             1       0.2  8342.6 -32687
## - CAR             1       0.2  8342.6 -32687
## - KC              1       0.3  8342.6 -32687
## - grass_1         1       0.3  8342.7 -32687
## - hot_weather     1       0.3  8342.7 -32687
## - TB              1       0.5  8342.8 -32686
## <none>                         8342.4 -32686
## - PHI             1       0.6  8343.0 -32686
## - home_team_1     1       0.7  8343.0 -32686
## - TEN             1       0.7  8343.0 -32686
## - ATL             1       0.7  8343.1 -32686
## - NE              1       0.7  8343.1 -32686
## - BAL             1       0.9  8343.2 -32685
## - MINN            1       0.9  8343.3 -32685
## - WAS             1       1.0  8343.4 -32685
## - ARI             1       1.1  8343.4 -32685
## - SD              1       1.3  8343.7 -32684
## - CLE             1       1.7  8344.1 -32682
## - CIN             1       1.8  8344.1 -32682
## - DET             1       2.1  8344.5 -32681
## - HOU             1       2.4  8344.8 -32680
## - STL             1       2.4  8344.8 -32680
## - NYG             1       2.9  8345.2 -32679
## - cold_weather    1       3.5  8345.9 -32676
## - DEN             1       5.1  8347.5 -32671
## - forty1          1      10.8  8353.2 -32652
## - avg_rbry_pos    1      30.3  8372.7 -32588
## - avg_rbry_plyr   1    8447.5 16789.9 -13465
## 
## Step:  AIC=-32687.88
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - avg_rectd_plyr  1       0.0  8342.4 -32690
## - avg_qbtdp_plyr  1       0.1  8342.5 -32690
## - JAC             1       0.1  8342.5 -32690
## - OAK             1       0.1  8342.5 -32690
## - CHI             1       0.1  8342.5 -32690
## - NOR             1       0.1  8342.5 -32690
## - DAL             1       0.1  8342.5 -32690
## - bad_weather_1   1       0.1  8342.5 -32689
## - height          1       0.2  8342.6 -32689
## - IND             1       0.2  8342.6 -32689
## - NYJ             1       0.2  8342.6 -32689
## - SEA             1       0.2  8342.6 -32689
## - CAR             1       0.2  8342.6 -32689
## - KC              1       0.2  8342.6 -32689
## - grass_1         1       0.3  8342.7 -32689
## - MIA             1       0.3  8342.7 -32689
## - hot_weather     1       0.3  8342.7 -32689
## - TB              1       0.6  8343.0 -32688
## - PHI             1       0.6  8343.0 -32688
## <none>                         8342.4 -32688
## - home_team_1     1       0.7  8343.1 -32688
## - TEN             1       0.8  8343.2 -32687
## - ATL             1       0.8  8343.2 -32687
## - NE              1       0.9  8343.3 -32687
## - MINN            1       0.9  8343.3 -32687
## - BAL             1       1.0  8343.4 -32686
## - WAS             1       1.1  8343.5 -32686
## - ARI             1       1.2  8343.6 -32686
## - SD              1       1.5  8343.9 -32685
## - CLE             1       2.0  8344.4 -32683
## - CIN             1       2.0  8344.4 -32683
## - DET             1       2.4  8344.8 -32682
## - HOU             1       2.8  8345.2 -32681
## - STL             1       2.8  8345.2 -32681
## - NYG             1       3.2  8345.6 -32679
## - cold_weather    1       3.5  8346.0 -32678
## - DEN             1       5.6  8348.0 -32671
## - forty1          1      10.9  8353.3 -32654
## - avg_rbry_pos    1      30.3  8372.7 -32590
## - avg_rbry_plyr   1    8448.2 16790.6 -13466
## 
## Step:  AIC=-32689.77
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - avg_qbtdp_plyr  1       0.1  8342.5 -32692
## - JAC             1       0.1  8342.5 -32691
## - OAK             1       0.1  8342.5 -32691
## - CHI             1       0.1  8342.5 -32691
## - NOR             1       0.1  8342.5 -32691
## - DAL             1       0.1  8342.5 -32691
## - bad_weather_1   1       0.1  8342.6 -32691
## - IND             1       0.2  8342.6 -32691
## - NYJ             1       0.2  8342.6 -32691
## - height          1       0.2  8342.6 -32691
## - SEA             1       0.2  8342.6 -32691
## - CAR             1       0.2  8342.6 -32691
## - KC              1       0.2  8342.7 -32691
## - grass_1         1       0.3  8342.7 -32691
## - MIA             1       0.3  8342.7 -32691
## - hot_weather     1       0.3  8342.8 -32691
## - TB              1       0.6  8343.0 -32690
## - PHI             1       0.6  8343.0 -32690
## <none>                         8342.4 -32690
## - home_team_1     1       0.7  8343.1 -32690
## - TEN             1       0.8  8343.2 -32689
## - ATL             1       0.8  8343.3 -32689
## - NE              1       0.8  8343.3 -32689
## - MINN            1       0.9  8343.3 -32689
## - BAL             1       1.1  8343.5 -32688
## - WAS             1       1.2  8343.6 -32688
## - ARI             1       1.3  8343.7 -32688
## - SD              1       1.5  8343.9 -32687
## - CLE             1       2.0  8344.4 -32685
## - CIN             1       2.0  8344.5 -32685
## - DET             1       2.4  8344.9 -32684
## - HOU             1       2.8  8345.2 -32683
## - STL             1       2.8  8345.3 -32682
## - NYG             1       3.2  8345.7 -32681
## - cold_weather    1       3.6  8346.0 -32680
## - DEN             1       5.6  8348.1 -32673
## - forty1          1      11.5  8354.0 -32654
## - avg_rbry_pos    1      34.6  8377.0 -32578
## - avg_rbry_plyr   1    8450.6 16793.0 -13464
## 
## Step:  AIC=-32691.55
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - JAC            1       0.1  8342.6 -32693
## - OAK            1       0.1  8342.6 -32693
## - CHI            1       0.1  8342.6 -32693
## - DAL            1       0.1  8342.6 -32693
## - NOR            1       0.1  8342.6 -32693
## - bad_weather_1  1       0.1  8342.6 -32693
## - IND            1       0.2  8342.7 -32693
## - NYJ            1       0.2  8342.7 -32693
## - SEA            1       0.2  8342.7 -32693
## - height         1       0.2  8342.7 -32693
## - CAR            1       0.2  8342.7 -32693
## - KC             1       0.2  8342.7 -32693
## - grass_1        1       0.3  8342.8 -32693
## - MIA            1       0.3  8342.8 -32693
## - hot_weather    1       0.3  8342.8 -32692
## - PHI            1       0.6  8343.1 -32692
## - TB             1       0.6  8343.1 -32692
## <none>                        8342.5 -32692
## - home_team_1    1       0.7  8343.2 -32691
## - TEN            1       0.8  8343.3 -32691
## - ATL            1       0.8  8343.3 -32691
## - NE             1       0.8  8343.3 -32691
## - MINN           1       0.9  8343.4 -32691
## - BAL            1       1.1  8343.6 -32690
## - WAS            1       1.2  8343.7 -32690
## - ARI            1       1.3  8343.8 -32689
## - SD             1       1.5  8344.0 -32689
## - CLE            1       2.0  8344.5 -32687
## - CIN            1       2.0  8344.5 -32687
## - DET            1       2.4  8344.9 -32686
## - HOU            1       2.8  8345.3 -32684
## - STL            1       2.9  8345.4 -32684
## - NYG            1       3.3  8345.8 -32683
## - cold_weather   1       3.6  8346.1 -32682
## - DEN            1       5.6  8348.1 -32675
## - forty1         1      12.9  8355.4 -32651
## - avg_rbry_pos   1      34.6  8377.1 -32580
## - avg_rbry_plyr  1    8496.8 16839.3 -13390
## 
## Step:  AIC=-32693.25
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - OAK            1       0.1  8342.7 -32695
## - CHI            1       0.1  8342.7 -32695
## - DAL            1       0.1  8342.7 -32695
## - IND            1       0.1  8342.7 -32695
## - bad_weather_1  1       0.1  8342.7 -32695
## - NOR            1       0.2  8342.8 -32695
## - height         1       0.2  8342.8 -32695
## - NYJ            1       0.2  8342.8 -32695
## - MIA            1       0.2  8342.8 -32694
## - SEA            1       0.2  8342.8 -32694
## - grass_1        1       0.3  8342.9 -32694
## - CAR            1       0.3  8342.9 -32694
## - KC             1       0.3  8342.9 -32694
## - hot_weather    1       0.3  8342.9 -32694
## - TB             1       0.5  8343.1 -32694
## <none>                        8342.6 -32693
## - home_team_1    1       0.7  8343.2 -32693
## - PHI            1       0.7  8343.3 -32693
## - TEN            1       0.7  8343.3 -32693
## - ATL            1       0.8  8343.4 -32693
## - NE             1       0.8  8343.4 -32693
## - BAL            1       1.0  8343.6 -32692
## - MINN           1       1.0  8343.6 -32692
## - WAS            1       1.1  8343.7 -32692
## - ARI            1       1.2  8343.8 -32691
## - SD             1       1.4  8344.0 -32691
## - CLE            1       1.9  8344.5 -32689
## - CIN            1       2.0  8344.5 -32689
## - DET            1       2.3  8344.9 -32688
## - HOU            1       2.7  8345.3 -32686
## - STL            1       2.8  8345.4 -32686
## - NYG            1       3.2  8345.8 -32685
## - cold_weather   1       3.5  8346.1 -32684
## - DEN            1       5.5  8348.1 -32677
## - forty1         1      12.9  8355.5 -32653
## - avg_rbry_pos   1      34.6  8377.2 -32581
## - avg_rbry_plyr  1    8497.6 16840.2 -13391
## 
## Step:  AIC=-32695.01
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + 
##     SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - CHI            1       0.1  8342.7 -32697
## - DAL            1       0.1  8342.7 -32697
## - IND            1       0.1  8342.8 -32697
## - bad_weather_1  1       0.1  8342.8 -32697
## - height         1       0.2  8342.9 -32696
## - MIA            1       0.2  8342.9 -32696
## - NOR            1       0.2  8342.9 -32696
## - grass_1        1       0.2  8342.9 -32696
## - NYJ            1       0.3  8342.9 -32696
## - SEA            1       0.3  8343.0 -32696
## - CAR            1       0.3  8343.0 -32696
## - hot_weather    1       0.3  8343.0 -32696
## - KC             1       0.4  8343.0 -32696
## - TB             1       0.5  8343.1 -32695
## <none>                        8342.7 -32695
## - home_team_1    1       0.6  8343.3 -32695
## - TEN            1       0.7  8343.3 -32695
## - ATL            1       0.7  8343.4 -32695
## - NE             1       0.7  8343.4 -32695
## - PHI            1       0.8  8343.5 -32694
## - BAL            1       0.9  8343.6 -32694
## - WAS            1       1.0  8343.7 -32694
## - ARI            1       1.1  8343.8 -32693
## - MINN           1       1.1  8343.8 -32693
## - SD             1       1.3  8344.0 -32693
## - CLE            1       1.9  8344.5 -32691
## - CIN            1       1.9  8344.5 -32691
## - DET            1       2.3  8344.9 -32690
## - HOU            1       2.7  8345.3 -32688
## - STL            1       2.7  8345.4 -32688
## - NYG            1       3.1  8345.8 -32687
## - cold_weather   1       3.4  8346.1 -32686
## - DEN            1       5.5  8348.2 -32679
## - forty1         1      12.9  8355.5 -32655
## - avg_rbry_pos   1      35.0  8377.6 -32582
## - avg_rbry_plyr  1    8510.3 16852.9 -13372
## 
## Step:  AIC=-32696.84
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DAL + DEN + DET + HOU + 
##     IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - DAL            1       0.0  8342.8 -32699
## - IND            1       0.1  8342.8 -32699
## - bad_weather_1  1       0.1  8342.8 -32698
## - MIA            1       0.2  8342.9 -32698
## - height         1       0.2  8342.9 -32698
## - grass_1        1       0.2  8343.0 -32698
## - NOR            1       0.2  8343.0 -32698
## - NYJ            1       0.3  8343.0 -32698
## - SEA            1       0.3  8343.1 -32698
## - hot_weather    1       0.3  8343.1 -32698
## - CAR            1       0.4  8343.1 -32698
## - KC             1       0.4  8343.1 -32698
## - TB             1       0.4  8343.2 -32697
## <none>                        8342.7 -32697
## - TEN            1       0.6  8343.4 -32697
## - home_team_1    1       0.6  8343.4 -32697
## - ATL            1       0.7  8343.4 -32697
## - NE             1       0.7  8343.4 -32697
## - PHI            1       0.9  8343.6 -32696
## - BAL            1       0.9  8343.6 -32696
## - WAS            1       1.0  8343.7 -32696
## - ARI            1       1.1  8343.8 -32695
## - MINN           1       1.2  8343.9 -32695
## - SD             1       1.3  8344.0 -32695
## - CLE            1       1.8  8344.5 -32693
## - CIN            1       1.8  8344.6 -32693
## - DET            1       2.2  8344.9 -32692
## - HOU            1       2.6  8345.3 -32690
## - STL            1       2.6  8345.4 -32690
## - NYG            1       3.0  8345.8 -32689
## - cold_weather   1       3.5  8346.2 -32687
## - DEN            1       5.4  8348.2 -32681
## - forty1         1      12.9  8355.6 -32657
## - avg_rbry_pos   1      34.9  8377.6 -32584
## - avg_rbry_plyr  1    8514.0 16856.7 -13368
## 
## Step:  AIC=-32698.69
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + IND + 
##     KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - IND            1       0.1  8342.8 -32700
## - bad_weather_1  1       0.1  8342.9 -32700
## - MIA            1       0.2  8342.9 -32700
## - height         1       0.2  8343.0 -32700
## - grass_1        1       0.3  8343.0 -32700
## - NOR            1       0.3  8343.0 -32700
## - hot_weather    1       0.3  8343.1 -32700
## - NYJ            1       0.4  8343.1 -32700
## - SEA            1       0.4  8343.1 -32699
## - TB             1       0.4  8343.2 -32699
## - CAR            1       0.4  8343.2 -32699
## - KC             1       0.4  8343.2 -32699
## <none>                        8342.8 -32699
## - TEN            1       0.6  8343.4 -32699
## - home_team_1    1       0.6  8343.4 -32699
## - ATL            1       0.6  8343.4 -32699
## - NE             1       0.6  8343.4 -32699
## - BAL            1       0.8  8343.6 -32698
## - WAS            1       0.9  8343.7 -32698
## - PHI            1       0.9  8343.7 -32698
## - ARI            1       1.0  8343.8 -32697
## - SD             1       1.2  8344.0 -32697
## - MINN           1       1.3  8344.1 -32696
## - CLE            1       1.8  8344.5 -32695
## - CIN            1       1.8  8344.6 -32695
## - DET            1       2.2  8344.9 -32694
## - HOU            1       2.6  8345.3 -32692
## - STL            1       2.6  8345.4 -32692
## - NYG            1       3.0  8345.8 -32691
## - cold_weather   1       3.4  8346.2 -32689
## - DEN            1       5.4  8348.2 -32683
## - forty1         1      12.9  8355.6 -32658
## - avg_rbry_pos   1      34.9  8377.7 -32586
## - avg_rbry_plyr  1    8515.5 16858.3 -13367
## 
## Step:  AIC=-32700.49
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - bad_weather_1  1       0.1  8342.9 -32702
## - MIA            1       0.1  8343.0 -32702
## - height         1       0.2  8343.0 -32702
## - grass_1        1       0.3  8343.1 -32701
## - NOR            1       0.3  8343.2 -32701
## - hot_weather    1       0.3  8343.2 -32701
## - TB             1       0.4  8343.2 -32701
## - NYJ            1       0.4  8343.2 -32701
## - SEA            1       0.4  8343.3 -32701
## - CAR            1       0.5  8343.3 -32701
## - KC             1       0.5  8343.3 -32701
## - TEN            1       0.6  8343.4 -32701
## - home_team_1    1       0.6  8343.4 -32701
## - ATL            1       0.6  8343.4 -32701
## - NE             1       0.6  8343.4 -32701
## <none>                        8342.8 -32700
## - BAL            1       0.8  8343.6 -32700
## - WAS            1       0.9  8343.7 -32700
## - PHI            1       1.0  8343.8 -32699
## - ARI            1       1.0  8343.8 -32699
## - SD             1       1.2  8344.0 -32699
## - MINN           1       1.4  8344.2 -32698
## - CLE            1       1.7  8344.6 -32697
## - CIN            1       1.7  8344.6 -32697
## - DET            1       2.1  8344.9 -32696
## - HOU            1       2.5  8345.3 -32694
## - STL            1       2.5  8345.4 -32694
## - NYG            1       2.9  8345.8 -32693
## - cold_weather   1       3.4  8346.2 -32691
## - DEN            1       5.3  8348.2 -32685
## - forty1         1      12.9  8355.7 -32660
## - avg_rbry_pos   1      34.8  8377.7 -32588
## - avg_rbry_plyr  1    8515.5 16858.3 -13369
## 
## Step:  AIC=-32702.07
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
## 
##                 Df Sum of Sq     RSS    AIC
## - MIA            1       0.1  8343.1 -32704
## - height         1       0.2  8343.1 -32703
## - grass_1        1       0.3  8343.2 -32703
## - NOR            1       0.3  8343.3 -32703
## - hot_weather    1       0.4  8343.3 -32703
## - TB             1       0.4  8343.3 -32703
## - NYJ            1       0.4  8343.3 -32703
## - SEA            1       0.4  8343.4 -32703
## - CAR            1       0.5  8343.4 -32703
## - KC             1       0.5  8343.4 -32702
## - TEN            1       0.6  8343.5 -32702
## - ATL            1       0.6  8343.5 -32702
## - home_team_1    1       0.6  8343.5 -32702
## <none>                        8342.9 -32702
## - NE             1       0.6  8343.6 -32702
## - BAL            1       0.8  8343.7 -32701
## - WAS            1       0.9  8343.8 -32701
## - ARI            1       1.0  8343.9 -32701
## - PHI            1       1.0  8344.0 -32701
## - SD             1       1.2  8344.1 -32700
## - MINN           1       1.4  8344.4 -32699
## - CIN            1       1.7  8344.7 -32698
## - CLE            1       1.7  8344.7 -32698
## - DET            1       2.1  8345.1 -32697
## - STL            1       2.5  8345.5 -32696
## - HOU            1       2.5  8345.5 -32696
## - NYG            1       3.0  8345.9 -32694
## - cold_weather   1       3.7  8346.6 -32692
## - DEN            1       5.3  8348.2 -32687
## - forty1         1      12.9  8355.9 -32662
## - avg_rbry_pos   1      34.9  8377.8 -32589
## - avg_rbry_plyr  1    8515.9 16858.8 -13370
## 
## Step:  AIC=-32703.65
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + 
##     MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
## 
##                 Df Sum of Sq     RSS    AIC
## - height         1       0.2  8343.3 -32705
## - grass_1        1       0.3  8343.4 -32705
## - TB             1       0.3  8343.4 -32705
## - hot_weather    1       0.4  8343.4 -32704
## - NOR            1       0.4  8343.5 -32704
## - NYJ            1       0.4  8343.5 -32704
## - SEA            1       0.5  8343.6 -32704
## - TEN            1       0.5  8343.6 -32704
## - CAR            1       0.5  8343.6 -32704
## - ATL            1       0.5  8343.6 -32704
## - KC             1       0.5  8343.6 -32704
## - NE             1       0.6  8343.6 -32704
## <none>                        8343.1 -32704
## - home_team_1    1       0.6  8343.7 -32704
## - BAL            1       0.7  8343.8 -32703
## - WAS            1       0.8  8343.9 -32703
## - ARI            1       0.9  8344.0 -32703
## - PHI            1       1.1  8344.2 -32702
## - SD             1       1.1  8344.2 -32702
## - MINN           1       1.5  8344.6 -32701
## - CIN            1       1.7  8344.7 -32700
## - CLE            1       1.7  8344.8 -32700
## - DET            1       2.0  8345.1 -32699
## - STL            1       2.4  8345.5 -32698
## - HOU            1       2.4  8345.5 -32698
## - NYG            1       2.9  8345.9 -32696
## - cold_weather   1       3.6  8346.7 -32694
## - DEN            1       5.2  8348.3 -32689
## - forty1         1      13.0  8356.0 -32663
## - avg_rbry_pos   1      34.9  8378.0 -32591
## - avg_rbry_plyr  1    8517.7 16860.7 -13369
## 
## Step:  AIC=-32705
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
## 
##                 Df Sum of Sq     RSS    AIC
## - grass_1        1       0.3  8343.6 -32706
## - TB             1       0.3  8343.6 -32706
## - hot_weather    1       0.4  8343.6 -32706
## - NOR            1       0.4  8343.6 -32706
## - NYJ            1       0.4  8343.7 -32706
## - SEA            1       0.5  8343.7 -32705
## - TEN            1       0.5  8343.8 -32705
## - CAR            1       0.5  8343.8 -32705
## - KC             1       0.5  8343.8 -32705
## - ATL            1       0.6  8343.8 -32705
## <none>                        8343.3 -32705
## - home_team_1    1       0.6  8343.9 -32705
## - NE             1       0.6  8343.9 -32705
## - BAL            1       0.7  8344.0 -32705
## - WAS            1       0.9  8344.1 -32704
## - ARI            1       0.9  8344.2 -32704
## - PHI            1       1.1  8344.3 -32704
## - SD             1       1.1  8344.4 -32703
## - MINN           1       1.5  8344.8 -32702
## - CIN            1       1.7  8345.0 -32701
## - CLE            1       1.7  8345.0 -32701
## - DET            1       2.0  8345.3 -32700
## - HOU            1       2.4  8345.7 -32699
## - STL            1       2.5  8345.7 -32699
## - NYG            1       2.9  8346.1 -32698
## - cold_weather   1       3.6  8346.9 -32695
## - DEN            1       5.2  8348.5 -32690
## - forty1         1      15.4  8358.7 -32656
## - avg_rbry_pos   1      45.2  8388.4 -32559
## - avg_rbry_plyr  1    8556.5 16899.8 -13307
## 
## Step:  AIC=-32706.08
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - NOR            1       0.3  8343.9 -32707
## - TB             1       0.3  8343.9 -32707
## - NYJ            1       0.4  8343.9 -32707
## - SEA            1       0.4  8343.9 -32707
## - hot_weather    1       0.4  8344.0 -32707
## - TEN            1       0.5  8344.0 -32707
## - home_team_1    1       0.5  8344.0 -32706
## - CAR            1       0.6  8344.1 -32706
## - KC             1       0.6  8344.2 -32706
## <none>                        8343.6 -32706
## - ATL            1       0.6  8344.2 -32706
## - NE             1       0.8  8344.3 -32706
## - BAL            1       0.8  8344.4 -32705
## - WAS            1       0.8  8344.4 -32705
## - ARI            1       1.0  8344.5 -32705
## - SD             1       1.0  8344.6 -32705
## - PHI            1       1.1  8344.7 -32704
## - MINN           1       1.4  8345.0 -32703
## - CLE            1       1.6  8345.2 -32703
## - CIN            1       1.9  8345.4 -32702
## - DET            1       2.2  8345.7 -32701
## - HOU            1       2.6  8346.1 -32700
## - STL            1       2.6  8346.2 -32699
## - NYG            1       3.1  8346.7 -32698
## - cold_weather   1       3.5  8347.1 -32696
## - DEN            1       5.1  8348.7 -32691
## - forty1         1      15.4  8359.0 -32657
## - avg_rbry_pos   1      45.1  8388.7 -32560
## - avg_rbry_plyr  1    8556.7 16900.2 -13309
## 
## Step:  AIC=-32707.06
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - NYJ            1       0.3  8344.2 -32708
## - SEA            1       0.3  8344.2 -32708
## - TB             1       0.4  8344.2 -32708
## - hot_weather    1       0.4  8344.3 -32708
## - CAR            1       0.5  8344.4 -32707
## - KC             1       0.5  8344.4 -32707
## - home_team_1    1       0.5  8344.4 -32707
## - TEN            1       0.6  8344.4 -32707
## <none>                        8343.9 -32707
## - ATL            1       0.7  8344.6 -32707
## - NE             1       0.9  8344.7 -32706
## - BAL            1       0.9  8344.8 -32706
## - WAS            1       0.9  8344.8 -32706
## - PHI            1       1.0  8344.9 -32706
## - ARI            1       1.1  8345.0 -32705
## - SD             1       1.2  8345.0 -32705
## - MINN           1       1.3  8345.2 -32705
## - CLE            1       1.8  8345.6 -32703
## - CIN            1       2.0  8345.9 -32702
## - DET            1       2.4  8346.3 -32701
## - HOU            1       2.8  8346.6 -32700
## - STL            1       2.8  8346.7 -32700
## - NYG            1       3.3  8347.2 -32698
## - cold_weather   1       3.6  8347.5 -32697
## - DEN            1       5.4  8349.2 -32691
## - forty1         1      15.5  8359.3 -32658
## - avg_rbry_pos   1      44.9  8388.8 -32561
## - avg_rbry_plyr  1    8570.1 16914.0 -13289
## 
## Step:  AIC=-32708.07
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NYG + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - SEA            1       0.3  8344.4 -32709
## - CAR            1       0.4  8344.6 -32709
## - TB             1       0.4  8344.6 -32709
## - hot_weather    1       0.4  8344.6 -32709
## - KC             1       0.5  8344.6 -32709
## - home_team_1    1       0.5  8344.7 -32708
## <none>                        8344.2 -32708
## - TEN            1       0.6  8344.8 -32708
## - ATL            1       0.8  8345.0 -32707
## - PHI            1       0.9  8345.1 -32707
## - NE             1       1.0  8345.1 -32707
## - BAL            1       1.0  8345.2 -32707
## - WAS            1       1.0  8345.2 -32707
## - MINN           1       1.2  8345.4 -32706
## - ARI            1       1.2  8345.4 -32706
## - SD             1       1.3  8345.4 -32706
## - CLE            1       1.9  8346.1 -32704
## - CIN            1       2.2  8346.4 -32703
## - DET            1       2.5  8346.7 -32702
## - HOU            1       2.9  8347.1 -32700
## - STL            1       3.0  8347.2 -32700
## - NYG            1       3.5  8347.7 -32698
## - cold_weather   1       3.6  8347.7 -32698
## - DEN            1       5.7  8349.8 -32691
## - forty1         1      15.5  8359.6 -32659
## - avg_rbry_pos   1      45.1  8389.2 -32562
## - avg_rbry_plyr  1    8572.8 16917.0 -13286
## 
## Step:  AIC=-32709.21
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - CAR            1       0.4  8344.8 -32710
## - KC             1       0.4  8344.8 -32710
## - hot_weather    1       0.5  8344.9 -32710
## - TB             1       0.5  8344.9 -32710
## - home_team_1    1       0.5  8344.9 -32710
## <none>                        8344.4 -32709
## - TEN            1       0.7  8345.1 -32709
## - PHI            1       0.9  8345.3 -32708
## - ATL            1       0.9  8345.3 -32708
## - NE             1       1.1  8345.5 -32708
## - BAL            1       1.1  8345.5 -32708
## - WAS            1       1.1  8345.6 -32707
## - MINN           1       1.1  8345.6 -32707
## - ARI            1       1.3  8345.7 -32707
## - SD             1       1.4  8345.8 -32707
## - CLE            1       2.0  8346.5 -32705
## - CIN            1       2.3  8346.8 -32704
## - DET            1       2.7  8347.1 -32702
## - HOU            1       3.1  8347.5 -32701
## - STL            1       3.1  8347.6 -32701
## - cold_weather   1       3.5  8347.9 -32700
## - NYG            1       3.7  8348.2 -32699
## - DEN            1       5.9  8350.3 -32692
## - forty1         1      15.6  8360.0 -32660
## - avg_rbry_pos   1      45.2  8389.6 -32563
## - avg_rbry_plyr  1    8574.3 16918.7 -13285
## 
## Step:  AIC=-32709.96
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CIN + CLE + DEN + DET + HOU + KC + MINN + NE + 
##     NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - KC             1       0.4  8345.2 -32711
## - hot_weather    1       0.5  8345.3 -32710
## - home_team_1    1       0.5  8345.3 -32710
## - TB             1       0.6  8345.4 -32710
## <none>                        8344.8 -32710
## - TEN            1       0.8  8345.6 -32709
## - PHI            1       0.8  8345.6 -32709
## - ATL            1       1.0  8345.8 -32709
## - MINN           1       1.1  8345.9 -32708
## - NE             1       1.2  8346.0 -32708
## - BAL            1       1.2  8346.0 -32708
## - WAS            1       1.2  8346.0 -32708
## - ARI            1       1.4  8346.2 -32707
## - SD             1       1.5  8346.3 -32707
## - CLE            1       2.2  8347.0 -32705
## - CIN            1       2.5  8347.3 -32704
## - DET            1       2.8  8347.6 -32703
## - HOU            1       3.2  8348.0 -32701
## - STL            1       3.3  8348.1 -32701
## - cold_weather   1       3.5  8348.3 -32700
## - NYG            1       3.9  8348.7 -32699
## - DEN            1       6.2  8351.0 -32692
## - forty1         1      15.6  8360.4 -32661
## - avg_rbry_pos   1      45.4  8390.2 -32563
## - avg_rbry_plyr  1    8575.7 16920.5 -13284
## 
## Step:  AIC=-32710.78
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CIN + CLE + DEN + DET + HOU + MINN + NE + NYG + 
##     PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - hot_weather    1       0.4  8345.6 -32711
## - home_team_1    1       0.4  8345.6 -32711
## <none>                        8345.2 -32711
## - TB             1       0.6  8345.8 -32711
## - PHI            1       0.7  8345.9 -32710
## - TEN            1       0.9  8346.0 -32710
## - MINN           1       1.0  8346.1 -32710
## - ATL            1       1.1  8346.2 -32709
## - NE             1       1.3  8346.4 -32709
## - BAL            1       1.3  8346.5 -32709
## - WAS            1       1.3  8346.5 -32708
## - ARI            1       1.5  8346.7 -32708
## - SD             1       1.6  8346.7 -32708
## - CLE            1       2.3  8347.5 -32705
## - CIN            1       2.6  8347.8 -32704
## - DET            1       2.9  8348.1 -32703
## - HOU            1       3.4  8348.5 -32702
## - STL            1       3.4  8348.6 -32701
## - cold_weather   1       3.5  8348.6 -32701
## - NYG            1       4.1  8349.3 -32699
## - DEN            1       6.4  8351.6 -32692
## - forty1         1      15.6  8360.8 -32661
## - avg_rbry_pos   1      45.3  8390.5 -32564
## - avg_rbry_plyr  1    8575.8 16921.0 -13285
## 
## Step:  AIC=-32711.31
## ra ~ cold_weather + home_team_1 + forty1 + ARI + ATL + BAL + 
##     CIN + CLE + DEN + DET + HOU + MINN + NE + NYG + PHI + SD + 
##     STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - home_team_1    1       0.4  8346.0 -32712
## - TB             1       0.6  8346.2 -32711
## <none>                        8345.6 -32711
## - PHI            1       0.7  8346.3 -32711
## - TEN            1       0.9  8346.5 -32710
## - MINN           1       1.0  8346.6 -32710
## - ATL            1       1.1  8346.7 -32710
## - NE             1       1.3  8346.9 -32709
## - BAL            1       1.3  8346.9 -32709
## - WAS            1       1.3  8347.0 -32709
## - SD             1       1.5  8347.1 -32708
## - ARI            1       1.5  8347.1 -32708
## - CLE            1       2.3  8347.9 -32706
## - CIN            1       2.6  8348.2 -32705
## - DET            1       3.0  8348.6 -32704
## - STL            1       3.4  8349.0 -32702
## - HOU            1       3.4  8349.0 -32702
## - cold_weather   1       3.5  8349.1 -32702
## - NYG            1       4.1  8349.7 -32700
## - DEN            1       6.4  8352.0 -32692
## - forty1         1      15.7  8361.3 -32662
## - avg_rbry_pos   1      45.4  8391.0 -32564
## - avg_rbry_plyr  1    8575.4 16921.0 -13287
## 
## Step:  AIC=-32711.86
## ra ~ cold_weather + forty1 + ARI + ATL + BAL + CIN + CLE + DEN + 
##     DET + HOU + MINN + NE + NYG + PHI + SD + STL + TB + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## <none>                        8346.0 -32712
## - TB             1       0.6  8346.7 -32712
## - PHI            1       0.7  8346.7 -32712
## - TEN            1       0.9  8347.0 -32711
## - ATL            1       0.9  8347.0 -32711
## - MINN           1       1.0  8347.0 -32711
## - NE             1       1.3  8347.4 -32709
## - ARI            1       1.3  8347.4 -32709
## - BAL            1       1.3  8347.4 -32709
## - WAS            1       1.4  8347.5 -32709
## - SD             1       1.5  8347.6 -32709
## - CLE            1       2.4  8348.4 -32706
## - CIN            1       2.7  8348.7 -32705
## - DET            1       2.8  8348.8 -32705
## - STL            1       3.2  8349.2 -32703
## - HOU            1       3.2  8349.2 -32703
## - cold_weather   1       3.8  8349.8 -32701
## - NYG            1       4.2  8350.2 -32700
## - DEN            1       6.5  8352.6 -32692
## - forty1         1      15.6  8361.7 -32662
## - avg_rbry_pos   1      45.4  8391.4 -32565
## - avg_rbry_plyr  1    8575.6 16921.6 -13288

TDR

PreProcess:

set.seed(123)
splitdr <- sample.split(nfl_data$tdr, SplitRatio = 0.7)
Traintdr <- subset(nfl_data, split == TRUE)
Testtdr <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Traintdr, method = c("center", "scale"))
trainTransformedtdr <- predict(preProcValues, Traintdr)
testTransformedtdr <- predict(preProcValues, Testtdr)

ggpairs:

ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("tdr",colnames(filtered_nfl_data_fields[46:51]))])

regression:

tdrregform <- formula(paste("ra ~ ", 
                           paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegtdr <- lm(tdrregform, data = trainTransformedtdr)
summary(linRegRushAtt)
## 
## Call:
## lm(formula = raregform, data = trainTransformedra)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8046 -0.0854 -0.0090  0.0496  5.3831 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      8.104e-15  3.326e-03   0.000 1.000000    
## height          -2.162e-03  6.453e-03  -0.335 0.737573    
## weight          -1.279e-03  6.048e-03  -0.212 0.832493    
## cold_weather     1.184e-02  3.501e-03   3.381 0.000724 ***
## hot_weather     -3.506e-03  3.356e-03  -1.045 0.296176    
## home_team_1      5.312e-03  3.619e-03   1.468 0.142168    
## forty1           2.705e-02  5.740e-03   4.712 2.46e-06 ***
## vertical1        2.959e-04  4.413e-03   0.067 0.946539    
## ARI              7.646e-03  4.653e-03   1.643 0.100312    
## ATL              6.424e-03  4.675e-03   1.374 0.169437    
## BAL              7.016e-03  4.679e-03   1.499 0.133760    
## BUF             -8.683e-04  4.619e-03  -0.188 0.850888    
## CAR             -2.889e-03  4.589e-03  -0.630 0.528932    
## CHI              2.194e-03  4.537e-03   0.483 0.628766    
## CIN              9.587e-03  4.621e-03   2.075 0.038017 *  
## CLE              9.419e-03  4.600e-03   2.048 0.040589 *  
## DAL              2.418e-03  4.646e-03   0.521 0.602708    
## DEN              1.599e-02  4.664e-03   3.429 0.000607 ***
## DET              1.059e-02  4.600e-03   2.302 0.021340 *  
## GB               5.605e-04  4.735e-03   0.118 0.905783    
## HOU              1.138e-02  4.679e-03   2.432 0.015023 *  
## IND              2.856e-03  4.645e-03   0.615 0.538603    
## JAC              2.146e-03  4.531e-03   0.474 0.635752    
## KC              -3.085e-03  4.630e-03  -0.666 0.505194    
## MIA              3.608e-03  4.556e-03   0.792 0.428412    
## MINN            -6.259e-03  4.584e-03  -1.365 0.172130    
## NE               6.544e-03  4.787e-03   1.367 0.171597    
## NOR             -1.954e-03  4.772e-03  -0.409 0.682181    
## NYG              1.218e-02  4.665e-03   2.611 0.009035 ** 
## NYJ             -2.709e-03  4.647e-03  -0.583 0.560015    
## OAK              2.270e-03  4.677e-03   0.485 0.627353    
## PHI             -4.940e-03  4.532e-03  -1.090 0.275639    
## PIT              1.039e-03  4.651e-03   0.223 0.823167    
## SD               8.241e-03  4.564e-03   1.806 0.070952 .  
## SEA             -2.708e-03  4.736e-03  -0.572 0.567490    
## STL              1.129e-02  4.610e-03   2.449 0.014334 *  
## TB               5.189e-03  4.567e-03   1.136 0.255896    
## TEN              6.032e-03  4.594e-03   1.313 0.189196    
## WAS              7.307e-03  4.619e-03   1.582 0.113631    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -1.540e-03  4.247e-03  -0.363 0.716951    
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr    7.971e-01  5.083e-03 156.823  < 2e-16 ***
## avg_rbry_pos     5.532e-02  5.922e-03   9.341  < 2e-16 ***
## avg_fuml_plyr    1.334e-03  4.913e-03   0.271 0.786013    
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -3.404e-03  5.337e-03  -0.638 0.523639    
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -3.779e-03  3.827e-03  -0.987 0.323445    
## bad_weather_1    2.234e-03  3.383e-03   0.660 0.509067    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5514 on 27438 degrees of freedom
## Multiple R-squared:  0.6965, Adjusted R-squared:  0.696 
## F-statistic:  1399 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegtdr2 <- update(linRegRushYd,~.-height-weight-hot_weather
                     -home_team_1-age-is_TE-vertical1-ARI-ATL-BAL - BUF - CAR - CHI
                         -CIN - CLE - DAL - GB - JAC - KC - MIA 
                         -MINN - NE - NOR -NYJ - OAK - PHI - PIT -SD - SEA 
                         -TB - TEN - WAS
                         -avg_rectd_plyr-avg_trg_team-avg_tdr_team-avg_rbra_team
                         -avg_fuml_team-avg_fuml_plyr-avg_qbints_team-avg_qbtdp_team-avg_qbints_plyr
                         -bad_weather_1-grass_1)

summary(linRegtdr2)
## 
## Call:
## lm(formula = ry ~ cold_weather + forty1 + DEN + DET + HOU + IND + 
##     NYG + STL + avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr, 
##     data = trainTransformedry)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4809 -0.0756 -0.0161  0.0145  7.1744 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.337e-14  3.912e-03   0.000 1.000000    
## cold_weather    1.434e-02  3.940e-03   3.641 0.000272 ***
## forty1         -2.918e-04  4.527e-03  -0.064 0.948609    
## DEN             7.798e-03  3.927e-03   1.986 0.047077 *  
## DET             4.884e-03  3.935e-03   1.241 0.214576    
## HOU             5.955e-03  3.938e-03   1.512 0.130493    
## IND            -2.975e-03  3.928e-03  -0.757 0.448787    
## NYG             6.068e-03  3.931e-03   1.543 0.122723    
## STL             4.319e-03  3.931e-03   1.099 0.271837    
## avg_rbry_plyr   7.584e-01  5.588e-03 135.721  < 2e-16 ***
## avg_rbry_pos    3.961e-03  5.522e-03   0.717 0.473119    
## avg_qbtdp_plyr -1.006e-03  4.461e-03  -0.226 0.821536    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6486 on 27472 degrees of freedom
## Multiple R-squared:  0.5795, Adjusted R-squared:  0.5793 
## F-statistic:  3441 on 11 and 27472 DF,  p-value: < 2.2e-16
linRegtdr3 <- update(linRegtdr2,~.-is_WR-is_TE-forty1-DET-HOU-NYG-STL-avg_rbry_pos)
summary(linRegtdr3)
## 
## Call:
## lm(formula = ry ~ cold_weather + DEN + IND + avg_rbry_plyr + 
##     avg_qbtdp_plyr, data = trainTransformedry)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4560 -0.0781 -0.0085  0.0082  7.1710 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     2.343e-14  3.912e-03   0.000 1.000000    
## cold_weather    1.375e-02  3.916e-03   3.512 0.000446 ***
## DEN             7.084e-03  3.917e-03   1.808 0.070553 .  
## IND            -3.724e-03  3.916e-03  -0.951 0.341701    
## avg_rbry_plyr   7.610e-01  3.913e-03 194.482  < 2e-16 ***
## avg_qbtdp_plyr -1.210e-03  3.913e-03  -0.309 0.757208    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6486 on 27478 degrees of freedom
## Multiple R-squared:  0.5794, Adjusted R-squared:  0.5793 
## F-statistic:  7569 on 5 and 27478 DF,  p-value: < 2.2e-16

Testing:

RushTdrPredicted <- predict(linRegtdr3, newdata = testTransformedtdr)

SSErutdr <- sum((RushTdrPredicted - testTransformedtdr$tdr)^2)
SSTrutdr <- sum((mean(nfl_data$tdr)-testTransformedtdr$tdr)^2)
r2_rutdr <- 1 - SSErutdr/SSTrutdr 
r2_rutdr
## [1] 0.08372787
rmse_rutdr <- sqrt(SSErutdr/nrow(testTransformedtdr))
rmse_rutdr
## [1] 0.9645189

Plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegtdr3, which = c(1:3,2))

Summary Statistics:

confint(linRegtdr3)
##                        2.5 %      97.5 %
## (Intercept)    -0.0076686590 0.007668659
## cold_weather    0.0060761053 0.021427471
## DEN            -0.0005940149 0.014762520
## IND            -0.0113994186 0.003952273
## avg_rbry_plyr   0.7532922619 0.768630653
## avg_qbtdp_plyr -0.0088797123 0.006460201
coef(summary(linRegtdr3))
##                     Estimate  Std. Error       t value     Pr(>|t|)
## (Intercept)     2.342949e-14 0.003912481  5.988396e-12 1.0000000000
## cold_weather    1.375179e-02 0.003916064  3.511635e+00 0.0004460732
## DEN             7.084252e-03 0.003917383  1.808415e+00 0.0705529133
## IND            -3.723573e-03 0.003916147 -9.508255e-01 0.3417013100
## avg_rbry_plyr   7.609615e-01 0.003912754  1.944823e+02 0.0000000000
## avg_qbtdp_plyr -1.209756e-03 0.003913143 -3.091520e-01 0.7572082541
anova(linRegtdr3)
## Analysis of Variance Table
## 
## Response: ry
##                   Df  Sum Sq Mean Sq    F value    Pr(>F)    
## cold_weather       1     7.5     7.5    17.7343 2.548e-05 ***
## DEN                1     0.1     0.1     0.3041   0.58133    
## IND                1     2.2     2.2     5.2589   0.02184 *  
## avg_rbry_plyr      1 15912.8 15912.8 37823.6618 < 2.2e-16 ***
## avg_qbtdp_plyr     1     0.0     0.0     0.0956   0.75721    
## Residuals      27478 11560.3     0.4                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_ra <- step(lm(tdrregform, data = trainTransformedtdr), direction = "backward")
## Start:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-32676.19
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - vertical1       1       0.0  8342.3 -32678
## - GB              1       0.0  8342.3 -32678
## - BUF             1       0.0  8342.3 -32678
## - weight          1       0.0  8342.3 -32678
## - PIT             1       0.0  8342.3 -32678
## - avg_fuml_plyr   1       0.0  8342.3 -32678
## - height          1       0.0  8342.3 -32678
## - avg_rectd_plyr  1       0.0  8342.3 -32678
## - NOR             1       0.1  8342.4 -32678
## - JAC             1       0.1  8342.4 -32678
## - CHI             1       0.1  8342.4 -32678
## - OAK             1       0.1  8342.4 -32678
## - DAL             1       0.1  8342.4 -32678
## - SEA             1       0.1  8342.4 -32678
## - NYJ             1       0.1  8342.4 -32678
## - IND             1       0.1  8342.4 -32678
## - CAR             1       0.1  8342.4 -32678
## - avg_qbtdp_plyr  1       0.1  8342.4 -32678
## - bad_weather_1   1       0.1  8342.4 -32678
## - KC              1       0.1  8342.4 -32678
## - MIA             1       0.2  8342.5 -32678
## - grass_1         1       0.3  8342.6 -32677
## - hot_weather     1       0.3  8342.6 -32677
## - PHI             1       0.4  8342.7 -32677
## - TB              1       0.4  8342.7 -32677
## - TEN             1       0.5  8342.8 -32676
## - MINN            1       0.6  8342.9 -32676
## - NE              1       0.6  8342.9 -32676
## - ATL             1       0.6  8342.9 -32676
## <none>                         8342.3 -32676
## - home_team_1     1       0.7  8343.0 -32676
## - BAL             1       0.7  8343.0 -32676
## - WAS             1       0.8  8343.1 -32676
## - ARI             1       0.8  8343.1 -32675
## - SD              1       1.0  8343.3 -32675
## - CLE             1       1.3  8343.6 -32674
## - CIN             1       1.3  8343.6 -32674
## - DET             1       1.6  8343.9 -32673
## - HOU             1       1.8  8344.1 -32672
## - STL             1       1.8  8344.1 -32672
## - NYG             1       2.1  8344.4 -32671
## - cold_weather    1       3.5  8345.8 -32667
## - DEN             1       3.6  8345.9 -32666
## - forty1          1       6.8  8349.1 -32656
## - avg_rbry_pos    1      26.5  8368.8 -32591
## - avg_rbry_plyr   1    7477.5 15819.8 -15091
## 
## Step:  AIC=-32678.18
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MIA + MINN + 
##     NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - GB              1       0.0  8342.3 -32680
## - BUF             1       0.0  8342.3 -32680
## - weight          1       0.0  8342.3 -32680
## - PIT             1       0.0  8342.3 -32680
## - avg_fuml_plyr   1       0.0  8342.3 -32680
## - height          1       0.0  8342.3 -32680
## - avg_rectd_plyr  1       0.0  8342.3 -32680
## - NOR             1       0.1  8342.4 -32680
## - JAC             1       0.1  8342.4 -32680
## - CHI             1       0.1  8342.4 -32680
## - OAK             1       0.1  8342.4 -32680
## - DAL             1       0.1  8342.4 -32680
## - SEA             1       0.1  8342.4 -32680
## - NYJ             1       0.1  8342.4 -32680
## - IND             1       0.1  8342.4 -32680
## - CAR             1       0.1  8342.4 -32680
## - avg_qbtdp_plyr  1       0.1  8342.4 -32680
## - bad_weather_1   1       0.1  8342.4 -32680
## - KC              1       0.1  8342.4 -32680
## - MIA             1       0.2  8342.5 -32680
## - grass_1         1       0.3  8342.6 -32679
## - hot_weather     1       0.3  8342.6 -32679
## - PHI             1       0.4  8342.7 -32679
## - TB              1       0.4  8342.7 -32679
## - TEN             1       0.5  8342.8 -32678
## - MINN            1       0.6  8342.9 -32678
## - NE              1       0.6  8342.9 -32678
## - ATL             1       0.6  8342.9 -32678
## <none>                         8342.3 -32678
## - home_team_1     1       0.7  8343.0 -32678
## - BAL             1       0.7  8343.0 -32678
## - WAS             1       0.8  8343.1 -32678
## - ARI             1       0.8  8343.1 -32677
## - SD              1       1.0  8343.3 -32677
## - CLE             1       1.3  8343.6 -32676
## - CIN             1       1.3  8343.6 -32676
## - DET             1       1.6  8343.9 -32675
## - HOU             1       1.8  8344.1 -32674
## - STL             1       1.8  8344.1 -32674
## - NYG             1       2.1  8344.4 -32673
## - cold_weather    1       3.5  8345.8 -32669
## - DEN             1       3.6  8345.9 -32668
## - forty1          1       9.1  8351.4 -32650
## - avg_rbry_pos    1      26.5  8368.8 -32593
## - avg_rbry_plyr   1    7498.1 15840.4 -15057
## 
## Step:  AIC=-32680.17
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - PIT             1       0.0  8342.3 -32682
## - weight          1       0.0  8342.3 -32682
## - avg_fuml_plyr   1       0.0  8342.3 -32682
## - BUF             1       0.0  8342.3 -32682
## - height          1       0.0  8342.3 -32682
## - avg_rectd_plyr  1       0.0  8342.4 -32682
## - JAC             1       0.1  8342.4 -32682
## - CHI             1       0.1  8342.4 -32682
## - OAK             1       0.1  8342.4 -32682
## - DAL             1       0.1  8342.4 -32682
## - NOR             1       0.1  8342.4 -32682
## - avg_qbtdp_plyr  1       0.1  8342.4 -32682
## - IND             1       0.1  8342.4 -32682
## - bad_weather_1   1       0.1  8342.4 -32682
## - SEA             1       0.2  8342.5 -32682
## - NYJ             1       0.2  8342.5 -32682
## - CAR             1       0.2  8342.5 -32682
## - KC              1       0.2  8342.5 -32681
## - MIA             1       0.2  8342.5 -32681
## - grass_1         1       0.3  8342.6 -32681
## - hot_weather     1       0.3  8342.6 -32681
## - TB              1       0.5  8342.8 -32681
## - PHI             1       0.5  8342.8 -32680
## <none>                         8342.3 -32680
## - TEN             1       0.6  8342.9 -32680
## - home_team_1     1       0.7  8343.0 -32680
## - ATL             1       0.7  8343.0 -32680
## - NE              1       0.7  8343.0 -32680
## - MINN            1       0.8  8343.1 -32680
## - BAL             1       0.8  8343.2 -32679
## - WAS             1       0.9  8343.3 -32679
## - ARI             1       1.0  8343.3 -32679
## - SD              1       1.2  8343.5 -32678
## - CLE             1       1.6  8343.9 -32677
## - CIN             1       1.6  8344.0 -32677
## - DET             1       2.0  8344.3 -32676
## - HOU             1       2.3  8344.6 -32675
## - STL             1       2.3  8344.6 -32675
## - NYG             1       2.7  8345.0 -32673
## - cold_weather    1       3.5  8345.8 -32671
## - DEN             1       4.7  8347.0 -32667
## - forty1          1       9.1  8351.4 -32652
## - avg_rbry_pos    1      26.6  8368.9 -32595
## - avg_rbry_plyr   1    7498.1 15840.4 -15059
## 
## Step:  AIC=-32682.13
## ra ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + HOU + IND + JAC + KC + MIA + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - weight          1       0.0  8342.3 -32684
## - avg_fuml_plyr   1       0.0  8342.3 -32684
## - height          1       0.0  8342.4 -32684
## - avg_rectd_plyr  1       0.0  8342.4 -32684
## - BUF             1       0.0  8342.4 -32684
## - JAC             1       0.1  8342.4 -32684
## - CHI             1       0.1  8342.4 -32684
## - OAK             1       0.1  8342.4 -32684
## - DAL             1       0.1  8342.4 -32684
## - IND             1       0.1  8342.4 -32684
## - avg_qbtdp_plyr  1       0.1  8342.4 -32684
## - NOR             1       0.1  8342.4 -32684
## - bad_weather_1   1       0.1  8342.5 -32684
## - MIA             1       0.2  8342.5 -32683
## - SEA             1       0.2  8342.5 -32683
## - NYJ             1       0.2  8342.5 -32683
## - CAR             1       0.2  8342.6 -32683
## - KC              1       0.3  8342.6 -32683
## - grass_1         1       0.3  8342.6 -32683
## - hot_weather     1       0.3  8342.7 -32683
## - TB              1       0.5  8342.8 -32683
## <none>                         8342.3 -32682
## - PHI             1       0.6  8343.0 -32682
## - TEN             1       0.7  8343.0 -32682
## - home_team_1     1       0.7  8343.0 -32682
## - ATL             1       0.7  8343.0 -32682
## - NE              1       0.7  8343.0 -32682
## - BAL             1       0.9  8343.2 -32681
## - MINN            1       1.0  8343.3 -32681
## - WAS             1       1.0  8343.3 -32681
## - ARI             1       1.0  8343.4 -32681
## - SD              1       1.3  8343.6 -32680
## - CLE             1       1.7  8344.0 -32679
## - CIN             1       1.7  8344.1 -32678
## - DET             1       2.1  8344.5 -32677
## - HOU             1       2.4  8344.7 -32676
## - STL             1       2.4  8344.7 -32676
## - NYG             1       2.8  8345.2 -32675
## - cold_weather    1       3.6  8345.9 -32672
## - DEN             1       5.1  8347.4 -32667
## - forty1          1       9.1  8351.4 -32654
## - avg_rbry_pos    1      26.6  8368.9 -32597
## - avg_rbry_plyr   1    7500.2 15842.6 -15057
## 
## Step:  AIC=-32684.09
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - avg_fuml_plyr   1       0.0  8342.4 -32686
## - BUF             1       0.0  8342.4 -32686
## - avg_rectd_plyr  1       0.0  8342.4 -32686
## - JAC             1       0.1  8342.4 -32686
## - CHI             1       0.1  8342.4 -32686
## - OAK             1       0.1  8342.4 -32686
## - DAL             1       0.1  8342.4 -32686
## - avg_qbtdp_plyr  1       0.1  8342.4 -32686
## - IND             1       0.1  8342.5 -32686
## - NOR             1       0.1  8342.5 -32686
## - bad_weather_1   1       0.1  8342.5 -32686
## - height          1       0.1  8342.5 -32686
## - MIA             1       0.2  8342.5 -32685
## - NYJ             1       0.2  8342.6 -32685
## - SEA             1       0.2  8342.6 -32685
## - CAR             1       0.3  8342.6 -32685
## - KC              1       0.3  8342.6 -32685
## - grass_1         1       0.3  8342.6 -32685
## - hot_weather     1       0.3  8342.7 -32685
## - TB              1       0.5  8342.8 -32685
## <none>                         8342.3 -32684
## - PHI             1       0.6  8343.0 -32684
## - home_team_1     1       0.7  8343.0 -32684
## - TEN             1       0.7  8343.0 -32684
## - ATL             1       0.7  8343.1 -32684
## - NE              1       0.7  8343.1 -32684
## - BAL             1       0.9  8343.2 -32683
## - MINN            1       1.0  8343.3 -32683
## - WAS             1       1.0  8343.3 -32683
## - ARI             1       1.0  8343.4 -32683
## - SD              1       1.3  8343.6 -32682
## - CLE             1       1.7  8344.0 -32680
## - CIN             1       1.8  8344.1 -32680
## - DET             1       2.1  8344.5 -32679
## - STL             1       2.4  8344.8 -32678
## - HOU             1       2.4  8344.8 -32678
## - NYG             1       2.9  8345.2 -32677
## - cold_weather    1       3.6  8345.9 -32674
## - DEN             1       5.1  8347.4 -32669
## - forty1          1      10.8  8353.2 -32650
## - avg_rbry_pos    1      30.3  8372.7 -32586
## - avg_rbry_plyr   1    7517.1 15859.5 -15030
## 
## Step:  AIC=-32686
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + 
##     NYJ + OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - BUF             1       0.0  8342.4 -32688
## - avg_rectd_plyr  1       0.0  8342.4 -32688
## - JAC             1       0.1  8342.4 -32688
## - OAK             1       0.1  8342.4 -32688
## - CHI             1       0.1  8342.4 -32688
## - DAL             1       0.1  8342.4 -32688
## - avg_qbtdp_plyr  1       0.1  8342.5 -32688
## - IND             1       0.1  8342.5 -32688
## - NOR             1       0.1  8342.5 -32688
## - bad_weather_1   1       0.1  8342.5 -32688
## - height          1       0.1  8342.5 -32688
## - NYJ             1       0.2  8342.6 -32687
## - MIA             1       0.2  8342.6 -32687
## - SEA             1       0.2  8342.6 -32687
## - CAR             1       0.2  8342.6 -32687
## - KC              1       0.3  8342.6 -32687
## - grass_1         1       0.3  8342.7 -32687
## - hot_weather     1       0.3  8342.7 -32687
## - TB              1       0.5  8342.8 -32686
## <none>                         8342.4 -32686
## - PHI             1       0.6  8343.0 -32686
## - home_team_1     1       0.7  8343.0 -32686
## - TEN             1       0.7  8343.0 -32686
## - ATL             1       0.7  8343.1 -32686
## - NE              1       0.7  8343.1 -32686
## - BAL             1       0.9  8343.2 -32685
## - MINN            1       0.9  8343.3 -32685
## - WAS             1       1.0  8343.4 -32685
## - ARI             1       1.1  8343.4 -32685
## - SD              1       1.3  8343.7 -32684
## - CLE             1       1.7  8344.1 -32682
## - CIN             1       1.8  8344.1 -32682
## - DET             1       2.1  8344.5 -32681
## - HOU             1       2.4  8344.8 -32680
## - STL             1       2.4  8344.8 -32680
## - NYG             1       2.9  8345.2 -32679
## - cold_weather    1       3.5  8345.9 -32676
## - DEN             1       5.1  8347.5 -32671
## - forty1          1      10.8  8353.2 -32652
## - avg_rbry_pos    1      30.3  8372.7 -32588
## - avg_rbry_plyr   1    8447.5 16789.9 -13465
## 
## Step:  AIC=-32687.88
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - avg_rectd_plyr  1       0.0  8342.4 -32690
## - avg_qbtdp_plyr  1       0.1  8342.5 -32690
## - JAC             1       0.1  8342.5 -32690
## - OAK             1       0.1  8342.5 -32690
## - CHI             1       0.1  8342.5 -32690
## - NOR             1       0.1  8342.5 -32690
## - DAL             1       0.1  8342.5 -32690
## - bad_weather_1   1       0.1  8342.5 -32689
## - height          1       0.2  8342.6 -32689
## - IND             1       0.2  8342.6 -32689
## - NYJ             1       0.2  8342.6 -32689
## - SEA             1       0.2  8342.6 -32689
## - CAR             1       0.2  8342.6 -32689
## - KC              1       0.2  8342.6 -32689
## - grass_1         1       0.3  8342.7 -32689
## - MIA             1       0.3  8342.7 -32689
## - hot_weather     1       0.3  8342.7 -32689
## - TB              1       0.6  8343.0 -32688
## - PHI             1       0.6  8343.0 -32688
## <none>                         8342.4 -32688
## - home_team_1     1       0.7  8343.1 -32688
## - TEN             1       0.8  8343.2 -32687
## - ATL             1       0.8  8343.2 -32687
## - NE              1       0.9  8343.3 -32687
## - MINN            1       0.9  8343.3 -32687
## - BAL             1       1.0  8343.4 -32686
## - WAS             1       1.1  8343.5 -32686
## - ARI             1       1.2  8343.6 -32686
## - SD              1       1.5  8343.9 -32685
## - CLE             1       2.0  8344.4 -32683
## - CIN             1       2.0  8344.4 -32683
## - DET             1       2.4  8344.8 -32682
## - HOU             1       2.8  8345.2 -32681
## - STL             1       2.8  8345.2 -32681
## - NYG             1       3.2  8345.6 -32679
## - cold_weather    1       3.5  8346.0 -32678
## - DEN             1       5.6  8348.0 -32671
## - forty1          1      10.9  8353.3 -32654
## - avg_rbry_pos    1      30.3  8372.7 -32590
## - avg_rbry_plyr   1    8448.2 16790.6 -13466
## 
## Step:  AIC=-32689.77
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq     RSS    AIC
## - avg_qbtdp_plyr  1       0.1  8342.5 -32692
## - JAC             1       0.1  8342.5 -32691
## - OAK             1       0.1  8342.5 -32691
## - CHI             1       0.1  8342.5 -32691
## - NOR             1       0.1  8342.5 -32691
## - DAL             1       0.1  8342.5 -32691
## - bad_weather_1   1       0.1  8342.6 -32691
## - IND             1       0.2  8342.6 -32691
## - NYJ             1       0.2  8342.6 -32691
## - height          1       0.2  8342.6 -32691
## - SEA             1       0.2  8342.6 -32691
## - CAR             1       0.2  8342.6 -32691
## - KC              1       0.2  8342.7 -32691
## - grass_1         1       0.3  8342.7 -32691
## - MIA             1       0.3  8342.7 -32691
## - hot_weather     1       0.3  8342.8 -32691
## - TB              1       0.6  8343.0 -32690
## - PHI             1       0.6  8343.0 -32690
## <none>                         8342.4 -32690
## - home_team_1     1       0.7  8343.1 -32690
## - TEN             1       0.8  8343.2 -32689
## - ATL             1       0.8  8343.3 -32689
## - NE              1       0.8  8343.3 -32689
## - MINN            1       0.9  8343.3 -32689
## - BAL             1       1.1  8343.5 -32688
## - WAS             1       1.2  8343.6 -32688
## - ARI             1       1.3  8343.7 -32688
## - SD              1       1.5  8343.9 -32687
## - CLE             1       2.0  8344.4 -32685
## - CIN             1       2.0  8344.5 -32685
## - DET             1       2.4  8344.9 -32684
## - HOU             1       2.8  8345.2 -32683
## - STL             1       2.8  8345.3 -32682
## - NYG             1       3.2  8345.7 -32681
## - cold_weather    1       3.6  8346.0 -32680
## - DEN             1       5.6  8348.1 -32673
## - forty1          1      11.5  8354.0 -32654
## - avg_rbry_pos    1      34.6  8377.0 -32578
## - avg_rbry_plyr   1    8450.6 16793.0 -13464
## 
## Step:  AIC=-32691.55
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + JAC + KC + MIA + MINN + NE + NOR + NYG + NYJ + 
##     OAK + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - JAC            1       0.1  8342.6 -32693
## - OAK            1       0.1  8342.6 -32693
## - CHI            1       0.1  8342.6 -32693
## - DAL            1       0.1  8342.6 -32693
## - NOR            1       0.1  8342.6 -32693
## - bad_weather_1  1       0.1  8342.6 -32693
## - IND            1       0.2  8342.7 -32693
## - NYJ            1       0.2  8342.7 -32693
## - SEA            1       0.2  8342.7 -32693
## - height         1       0.2  8342.7 -32693
## - CAR            1       0.2  8342.7 -32693
## - KC             1       0.2  8342.7 -32693
## - grass_1        1       0.3  8342.8 -32693
## - MIA            1       0.3  8342.8 -32693
## - hot_weather    1       0.3  8342.8 -32692
## - PHI            1       0.6  8343.1 -32692
## - TB             1       0.6  8343.1 -32692
## <none>                        8342.5 -32692
## - home_team_1    1       0.7  8343.2 -32691
## - TEN            1       0.8  8343.3 -32691
## - ATL            1       0.8  8343.3 -32691
## - NE             1       0.8  8343.3 -32691
## - MINN           1       0.9  8343.4 -32691
## - BAL            1       1.1  8343.6 -32690
## - WAS            1       1.2  8343.7 -32690
## - ARI            1       1.3  8343.8 -32689
## - SD             1       1.5  8344.0 -32689
## - CLE            1       2.0  8344.5 -32687
## - CIN            1       2.0  8344.5 -32687
## - DET            1       2.4  8344.9 -32686
## - HOU            1       2.8  8345.3 -32684
## - STL            1       2.9  8345.4 -32684
## - NYG            1       3.3  8345.8 -32683
## - cold_weather   1       3.6  8346.1 -32682
## - DEN            1       5.6  8348.1 -32675
## - forty1         1      12.9  8355.4 -32651
## - avg_rbry_pos   1      34.6  8377.1 -32580
## - avg_rbry_plyr  1    8496.8 16839.3 -13390
## 
## Step:  AIC=-32693.25
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + OAK + 
##     PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - OAK            1       0.1  8342.7 -32695
## - CHI            1       0.1  8342.7 -32695
## - DAL            1       0.1  8342.7 -32695
## - IND            1       0.1  8342.7 -32695
## - bad_weather_1  1       0.1  8342.7 -32695
## - NOR            1       0.2  8342.8 -32695
## - height         1       0.2  8342.8 -32695
## - NYJ            1       0.2  8342.8 -32695
## - MIA            1       0.2  8342.8 -32694
## - SEA            1       0.2  8342.8 -32694
## - grass_1        1       0.3  8342.9 -32694
## - CAR            1       0.3  8342.9 -32694
## - KC             1       0.3  8342.9 -32694
## - hot_weather    1       0.3  8342.9 -32694
## - TB             1       0.5  8343.1 -32694
## <none>                        8342.6 -32693
## - home_team_1    1       0.7  8343.2 -32693
## - PHI            1       0.7  8343.3 -32693
## - TEN            1       0.7  8343.3 -32693
## - ATL            1       0.8  8343.4 -32693
## - NE             1       0.8  8343.4 -32693
## - BAL            1       1.0  8343.6 -32692
## - MINN           1       1.0  8343.6 -32692
## - WAS            1       1.1  8343.7 -32692
## - ARI            1       1.2  8343.8 -32691
## - SD             1       1.4  8344.0 -32691
## - CLE            1       1.9  8344.5 -32689
## - CIN            1       2.0  8344.5 -32689
## - DET            1       2.3  8344.9 -32688
## - HOU            1       2.7  8345.3 -32686
## - STL            1       2.8  8345.4 -32686
## - NYG            1       3.2  8345.8 -32685
## - cold_weather   1       3.5  8346.1 -32684
## - DEN            1       5.5  8348.1 -32677
## - forty1         1      12.9  8355.5 -32653
## - avg_rbry_pos   1      34.6  8377.2 -32581
## - avg_rbry_plyr  1    8497.6 16840.2 -13391
## 
## Step:  AIC=-32695.01
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CHI + CIN + CLE + DAL + DEN + DET + 
##     HOU + IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + 
##     SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - CHI            1       0.1  8342.7 -32697
## - DAL            1       0.1  8342.7 -32697
## - IND            1       0.1  8342.8 -32697
## - bad_weather_1  1       0.1  8342.8 -32697
## - height         1       0.2  8342.9 -32696
## - MIA            1       0.2  8342.9 -32696
## - NOR            1       0.2  8342.9 -32696
## - grass_1        1       0.2  8342.9 -32696
## - NYJ            1       0.3  8342.9 -32696
## - SEA            1       0.3  8343.0 -32696
## - CAR            1       0.3  8343.0 -32696
## - hot_weather    1       0.3  8343.0 -32696
## - KC             1       0.4  8343.0 -32696
## - TB             1       0.5  8343.1 -32695
## <none>                        8342.7 -32695
## - home_team_1    1       0.6  8343.3 -32695
## - TEN            1       0.7  8343.3 -32695
## - ATL            1       0.7  8343.4 -32695
## - NE             1       0.7  8343.4 -32695
## - PHI            1       0.8  8343.5 -32694
## - BAL            1       0.9  8343.6 -32694
## - WAS            1       1.0  8343.7 -32694
## - ARI            1       1.1  8343.8 -32693
## - MINN           1       1.1  8343.8 -32693
## - SD             1       1.3  8344.0 -32693
## - CLE            1       1.9  8344.5 -32691
## - CIN            1       1.9  8344.5 -32691
## - DET            1       2.3  8344.9 -32690
## - HOU            1       2.7  8345.3 -32688
## - STL            1       2.7  8345.4 -32688
## - NYG            1       3.1  8345.8 -32687
## - cold_weather   1       3.4  8346.1 -32686
## - DEN            1       5.5  8348.2 -32679
## - forty1         1      12.9  8355.5 -32655
## - avg_rbry_pos   1      35.0  8377.6 -32582
## - avg_rbry_plyr  1    8510.3 16852.9 -13372
## 
## Step:  AIC=-32696.84
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DAL + DEN + DET + HOU + 
##     IND + KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + 
##     grass_1 + bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - DAL            1       0.0  8342.8 -32699
## - IND            1       0.1  8342.8 -32699
## - bad_weather_1  1       0.1  8342.8 -32698
## - MIA            1       0.2  8342.9 -32698
## - height         1       0.2  8342.9 -32698
## - grass_1        1       0.2  8343.0 -32698
## - NOR            1       0.2  8343.0 -32698
## - NYJ            1       0.3  8343.0 -32698
## - SEA            1       0.3  8343.1 -32698
## - hot_weather    1       0.3  8343.1 -32698
## - CAR            1       0.4  8343.1 -32698
## - KC             1       0.4  8343.1 -32698
## - TB             1       0.4  8343.2 -32697
## <none>                        8342.7 -32697
## - TEN            1       0.6  8343.4 -32697
## - home_team_1    1       0.6  8343.4 -32697
## - ATL            1       0.7  8343.4 -32697
## - NE             1       0.7  8343.4 -32697
## - PHI            1       0.9  8343.6 -32696
## - BAL            1       0.9  8343.6 -32696
## - WAS            1       1.0  8343.7 -32696
## - ARI            1       1.1  8343.8 -32695
## - MINN           1       1.2  8343.9 -32695
## - SD             1       1.3  8344.0 -32695
## - CLE            1       1.8  8344.5 -32693
## - CIN            1       1.8  8344.6 -32693
## - DET            1       2.2  8344.9 -32692
## - HOU            1       2.6  8345.3 -32690
## - STL            1       2.6  8345.4 -32690
## - NYG            1       3.0  8345.8 -32689
## - cold_weather   1       3.5  8346.2 -32687
## - DEN            1       5.4  8348.2 -32681
## - forty1         1      12.9  8355.6 -32657
## - avg_rbry_pos   1      34.9  8377.6 -32584
## - avg_rbry_plyr  1    8514.0 16856.7 -13368
## 
## Step:  AIC=-32698.69
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + IND + 
##     KC + MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - IND            1       0.1  8342.8 -32700
## - bad_weather_1  1       0.1  8342.9 -32700
## - MIA            1       0.2  8342.9 -32700
## - height         1       0.2  8343.0 -32700
## - grass_1        1       0.3  8343.0 -32700
## - NOR            1       0.3  8343.0 -32700
## - hot_weather    1       0.3  8343.1 -32700
## - NYJ            1       0.4  8343.1 -32700
## - SEA            1       0.4  8343.1 -32699
## - TB             1       0.4  8343.2 -32699
## - CAR            1       0.4  8343.2 -32699
## - KC             1       0.4  8343.2 -32699
## <none>                        8342.8 -32699
## - TEN            1       0.6  8343.4 -32699
## - home_team_1    1       0.6  8343.4 -32699
## - ATL            1       0.6  8343.4 -32699
## - NE             1       0.6  8343.4 -32699
## - BAL            1       0.8  8343.6 -32698
## - WAS            1       0.9  8343.7 -32698
## - PHI            1       0.9  8343.7 -32698
## - ARI            1       1.0  8343.8 -32697
## - SD             1       1.2  8344.0 -32697
## - MINN           1       1.3  8344.1 -32696
## - CLE            1       1.8  8344.5 -32695
## - CIN            1       1.8  8344.6 -32695
## - DET            1       2.2  8344.9 -32694
## - HOU            1       2.6  8345.3 -32692
## - STL            1       2.6  8345.4 -32692
## - NYG            1       3.0  8345.8 -32691
## - cold_weather   1       3.4  8346.2 -32689
## - DEN            1       5.4  8348.2 -32683
## - forty1         1      12.9  8355.6 -32658
## - avg_rbry_pos   1      34.9  8377.7 -32586
## - avg_rbry_plyr  1    8515.5 16858.3 -13367
## 
## Step:  AIC=-32700.49
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1 + 
##     bad_weather_1
## 
##                 Df Sum of Sq     RSS    AIC
## - bad_weather_1  1       0.1  8342.9 -32702
## - MIA            1       0.1  8343.0 -32702
## - height         1       0.2  8343.0 -32702
## - grass_1        1       0.3  8343.1 -32701
## - NOR            1       0.3  8343.2 -32701
## - hot_weather    1       0.3  8343.2 -32701
## - TB             1       0.4  8343.2 -32701
## - NYJ            1       0.4  8343.2 -32701
## - SEA            1       0.4  8343.3 -32701
## - CAR            1       0.5  8343.3 -32701
## - KC             1       0.5  8343.3 -32701
## - TEN            1       0.6  8343.4 -32701
## - home_team_1    1       0.6  8343.4 -32701
## - ATL            1       0.6  8343.4 -32701
## - NE             1       0.6  8343.4 -32701
## <none>                        8342.8 -32700
## - BAL            1       0.8  8343.6 -32700
## - WAS            1       0.9  8343.7 -32700
## - PHI            1       1.0  8343.8 -32699
## - ARI            1       1.0  8343.8 -32699
## - SD             1       1.2  8344.0 -32699
## - MINN           1       1.4  8344.2 -32698
## - CLE            1       1.7  8344.6 -32697
## - CIN            1       1.7  8344.6 -32697
## - DET            1       2.1  8344.9 -32696
## - HOU            1       2.5  8345.3 -32694
## - STL            1       2.5  8345.4 -32694
## - NYG            1       2.9  8345.8 -32693
## - cold_weather   1       3.4  8346.2 -32691
## - DEN            1       5.3  8348.2 -32685
## - forty1         1      12.9  8355.7 -32660
## - avg_rbry_pos   1      34.8  8377.7 -32588
## - avg_rbry_plyr  1    8515.5 16858.3 -13369
## 
## Step:  AIC=-32702.07
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + 
##     TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
## 
##                 Df Sum of Sq     RSS    AIC
## - MIA            1       0.1  8343.1 -32704
## - height         1       0.2  8343.1 -32703
## - grass_1        1       0.3  8343.2 -32703
## - NOR            1       0.3  8343.3 -32703
## - hot_weather    1       0.4  8343.3 -32703
## - TB             1       0.4  8343.3 -32703
## - NYJ            1       0.4  8343.3 -32703
## - SEA            1       0.4  8343.4 -32703
## - CAR            1       0.5  8343.4 -32703
## - KC             1       0.5  8343.4 -32702
## - TEN            1       0.6  8343.5 -32702
## - ATL            1       0.6  8343.5 -32702
## - home_team_1    1       0.6  8343.5 -32702
## <none>                        8342.9 -32702
## - NE             1       0.6  8343.6 -32702
## - BAL            1       0.8  8343.7 -32701
## - WAS            1       0.9  8343.8 -32701
## - ARI            1       1.0  8343.9 -32701
## - PHI            1       1.0  8344.0 -32701
## - SD             1       1.2  8344.1 -32700
## - MINN           1       1.4  8344.4 -32699
## - CIN            1       1.7  8344.7 -32698
## - CLE            1       1.7  8344.7 -32698
## - DET            1       2.1  8345.1 -32697
## - STL            1       2.5  8345.5 -32696
## - HOU            1       2.5  8345.5 -32696
## - NYG            1       3.0  8345.9 -32694
## - cold_weather   1       3.7  8346.6 -32692
## - DEN            1       5.3  8348.2 -32687
## - forty1         1      12.9  8355.9 -32662
## - avg_rbry_pos   1      34.9  8377.8 -32589
## - avg_rbry_plyr  1    8515.9 16858.8 -13370
## 
## Step:  AIC=-32703.65
## ra ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     ARI + ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + 
##     MINN + NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
## 
##                 Df Sum of Sq     RSS    AIC
## - height         1       0.2  8343.3 -32705
## - grass_1        1       0.3  8343.4 -32705
## - TB             1       0.3  8343.4 -32705
## - hot_weather    1       0.4  8343.4 -32704
## - NOR            1       0.4  8343.5 -32704
## - NYJ            1       0.4  8343.5 -32704
## - SEA            1       0.5  8343.6 -32704
## - TEN            1       0.5  8343.6 -32704
## - CAR            1       0.5  8343.6 -32704
## - ATL            1       0.5  8343.6 -32704
## - KC             1       0.5  8343.6 -32704
## - NE             1       0.6  8343.6 -32704
## <none>                        8343.1 -32704
## - home_team_1    1       0.6  8343.7 -32704
## - BAL            1       0.7  8343.8 -32703
## - WAS            1       0.8  8343.9 -32703
## - ARI            1       0.9  8344.0 -32703
## - PHI            1       1.1  8344.2 -32702
## - SD             1       1.1  8344.2 -32702
## - MINN           1       1.5  8344.6 -32701
## - CIN            1       1.7  8344.7 -32700
## - CLE            1       1.7  8344.8 -32700
## - DET            1       2.0  8345.1 -32699
## - STL            1       2.4  8345.5 -32698
## - HOU            1       2.4  8345.5 -32698
## - NYG            1       2.9  8345.9 -32696
## - cold_weather   1       3.6  8346.7 -32694
## - DEN            1       5.2  8348.3 -32689
## - forty1         1      13.0  8356.0 -32663
## - avg_rbry_pos   1      34.9  8378.0 -32591
## - avg_rbry_plyr  1    8517.7 16860.7 -13369
## 
## Step:  AIC=-32705
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos + grass_1
## 
##                 Df Sum of Sq     RSS    AIC
## - grass_1        1       0.3  8343.6 -32706
## - TB             1       0.3  8343.6 -32706
## - hot_weather    1       0.4  8343.6 -32706
## - NOR            1       0.4  8343.6 -32706
## - NYJ            1       0.4  8343.7 -32706
## - SEA            1       0.5  8343.7 -32705
## - TEN            1       0.5  8343.8 -32705
## - CAR            1       0.5  8343.8 -32705
## - KC             1       0.5  8343.8 -32705
## - ATL            1       0.6  8343.8 -32705
## <none>                        8343.3 -32705
## - home_team_1    1       0.6  8343.9 -32705
## - NE             1       0.6  8343.9 -32705
## - BAL            1       0.7  8344.0 -32705
## - WAS            1       0.9  8344.1 -32704
## - ARI            1       0.9  8344.2 -32704
## - PHI            1       1.1  8344.3 -32704
## - SD             1       1.1  8344.4 -32703
## - MINN           1       1.5  8344.8 -32702
## - CIN            1       1.7  8345.0 -32701
## - CLE            1       1.7  8345.0 -32701
## - DET            1       2.0  8345.3 -32700
## - HOU            1       2.4  8345.7 -32699
## - STL            1       2.5  8345.7 -32699
## - NYG            1       2.9  8346.1 -32698
## - cold_weather   1       3.6  8346.9 -32695
## - DEN            1       5.2  8348.5 -32690
## - forty1         1      15.4  8358.7 -32656
## - avg_rbry_pos   1      45.2  8388.4 -32559
## - avg_rbry_plyr  1    8556.5 16899.8 -13307
## 
## Step:  AIC=-32706.08
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NOR + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - NOR            1       0.3  8343.9 -32707
## - TB             1       0.3  8343.9 -32707
## - NYJ            1       0.4  8343.9 -32707
## - SEA            1       0.4  8343.9 -32707
## - hot_weather    1       0.4  8344.0 -32707
## - TEN            1       0.5  8344.0 -32707
## - home_team_1    1       0.5  8344.0 -32706
## - CAR            1       0.6  8344.1 -32706
## - KC             1       0.6  8344.2 -32706
## <none>                        8343.6 -32706
## - ATL            1       0.6  8344.2 -32706
## - NE             1       0.8  8344.3 -32706
## - BAL            1       0.8  8344.4 -32705
## - WAS            1       0.8  8344.4 -32705
## - ARI            1       1.0  8344.5 -32705
## - SD             1       1.0  8344.6 -32705
## - PHI            1       1.1  8344.7 -32704
## - MINN           1       1.4  8345.0 -32703
## - CLE            1       1.6  8345.2 -32703
## - CIN            1       1.9  8345.4 -32702
## - DET            1       2.2  8345.7 -32701
## - HOU            1       2.6  8346.1 -32700
## - STL            1       2.6  8346.2 -32699
## - NYG            1       3.1  8346.7 -32698
## - cold_weather   1       3.5  8347.1 -32696
## - DEN            1       5.1  8348.7 -32691
## - forty1         1      15.4  8359.0 -32657
## - avg_rbry_pos   1      45.1  8388.7 -32560
## - avg_rbry_plyr  1    8556.7 16900.2 -13309
## 
## Step:  AIC=-32707.06
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NYG + NYJ + PHI + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - NYJ            1       0.3  8344.2 -32708
## - SEA            1       0.3  8344.2 -32708
## - TB             1       0.4  8344.2 -32708
## - hot_weather    1       0.4  8344.3 -32708
## - CAR            1       0.5  8344.4 -32707
## - KC             1       0.5  8344.4 -32707
## - home_team_1    1       0.5  8344.4 -32707
## - TEN            1       0.6  8344.4 -32707
## <none>                        8343.9 -32707
## - ATL            1       0.7  8344.6 -32707
## - NE             1       0.9  8344.7 -32706
## - BAL            1       0.9  8344.8 -32706
## - WAS            1       0.9  8344.8 -32706
## - PHI            1       1.0  8344.9 -32706
## - ARI            1       1.1  8345.0 -32705
## - SD             1       1.2  8345.0 -32705
## - MINN           1       1.3  8345.2 -32705
## - CLE            1       1.8  8345.6 -32703
## - CIN            1       2.0  8345.9 -32702
## - DET            1       2.4  8346.3 -32701
## - HOU            1       2.8  8346.6 -32700
## - STL            1       2.8  8346.7 -32700
## - NYG            1       3.3  8347.2 -32698
## - cold_weather   1       3.6  8347.5 -32697
## - DEN            1       5.4  8349.2 -32691
## - forty1         1      15.5  8359.3 -32658
## - avg_rbry_pos   1      44.9  8388.8 -32561
## - avg_rbry_plyr  1    8570.1 16914.0 -13289
## 
## Step:  AIC=-32708.07
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NYG + PHI + SD + SEA + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - SEA            1       0.3  8344.4 -32709
## - CAR            1       0.4  8344.6 -32709
## - TB             1       0.4  8344.6 -32709
## - hot_weather    1       0.4  8344.6 -32709
## - KC             1       0.5  8344.6 -32709
## - home_team_1    1       0.5  8344.7 -32708
## <none>                        8344.2 -32708
## - TEN            1       0.6  8344.8 -32708
## - ATL            1       0.8  8345.0 -32707
## - PHI            1       0.9  8345.1 -32707
## - NE             1       1.0  8345.1 -32707
## - BAL            1       1.0  8345.2 -32707
## - WAS            1       1.0  8345.2 -32707
## - MINN           1       1.2  8345.4 -32706
## - ARI            1       1.2  8345.4 -32706
## - SD             1       1.3  8345.4 -32706
## - CLE            1       1.9  8346.1 -32704
## - CIN            1       2.2  8346.4 -32703
## - DET            1       2.5  8346.7 -32702
## - HOU            1       2.9  8347.1 -32700
## - STL            1       3.0  8347.2 -32700
## - NYG            1       3.5  8347.7 -32698
## - cold_weather   1       3.6  8347.7 -32698
## - DEN            1       5.7  8349.8 -32691
## - forty1         1      15.5  8359.6 -32659
## - avg_rbry_pos   1      45.1  8389.2 -32562
## - avg_rbry_plyr  1    8572.8 16917.0 -13286
## 
## Step:  AIC=-32709.21
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CAR + CIN + CLE + DEN + DET + HOU + KC + MINN + 
##     NE + NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - CAR            1       0.4  8344.8 -32710
## - KC             1       0.4  8344.8 -32710
## - hot_weather    1       0.5  8344.9 -32710
## - TB             1       0.5  8344.9 -32710
## - home_team_1    1       0.5  8344.9 -32710
## <none>                        8344.4 -32709
## - TEN            1       0.7  8345.1 -32709
## - PHI            1       0.9  8345.3 -32708
## - ATL            1       0.9  8345.3 -32708
## - NE             1       1.1  8345.5 -32708
## - BAL            1       1.1  8345.5 -32708
## - WAS            1       1.1  8345.6 -32707
## - MINN           1       1.1  8345.6 -32707
## - ARI            1       1.3  8345.7 -32707
## - SD             1       1.4  8345.8 -32707
## - CLE            1       2.0  8346.5 -32705
## - CIN            1       2.3  8346.8 -32704
## - DET            1       2.7  8347.1 -32702
## - HOU            1       3.1  8347.5 -32701
## - STL            1       3.1  8347.6 -32701
## - cold_weather   1       3.5  8347.9 -32700
## - NYG            1       3.7  8348.2 -32699
## - DEN            1       5.9  8350.3 -32692
## - forty1         1      15.6  8360.0 -32660
## - avg_rbry_pos   1      45.2  8389.6 -32563
## - avg_rbry_plyr  1    8574.3 16918.7 -13285
## 
## Step:  AIC=-32709.96
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CIN + CLE + DEN + DET + HOU + KC + MINN + NE + 
##     NYG + PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - KC             1       0.4  8345.2 -32711
## - hot_weather    1       0.5  8345.3 -32710
## - home_team_1    1       0.5  8345.3 -32710
## - TB             1       0.6  8345.4 -32710
## <none>                        8344.8 -32710
## - TEN            1       0.8  8345.6 -32709
## - PHI            1       0.8  8345.6 -32709
## - ATL            1       1.0  8345.8 -32709
## - MINN           1       1.1  8345.9 -32708
## - NE             1       1.2  8346.0 -32708
## - BAL            1       1.2  8346.0 -32708
## - WAS            1       1.2  8346.0 -32708
## - ARI            1       1.4  8346.2 -32707
## - SD             1       1.5  8346.3 -32707
## - CLE            1       2.2  8347.0 -32705
## - CIN            1       2.5  8347.3 -32704
## - DET            1       2.8  8347.6 -32703
## - HOU            1       3.2  8348.0 -32701
## - STL            1       3.3  8348.1 -32701
## - cold_weather   1       3.5  8348.3 -32700
## - NYG            1       3.9  8348.7 -32699
## - DEN            1       6.2  8351.0 -32692
## - forty1         1      15.6  8360.4 -32661
## - avg_rbry_pos   1      45.4  8390.2 -32563
## - avg_rbry_plyr  1    8575.7 16920.5 -13284
## 
## Step:  AIC=-32710.78
## ra ~ cold_weather + hot_weather + home_team_1 + forty1 + ARI + 
##     ATL + BAL + CIN + CLE + DEN + DET + HOU + MINN + NE + NYG + 
##     PHI + SD + STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - hot_weather    1       0.4  8345.6 -32711
## - home_team_1    1       0.4  8345.6 -32711
## <none>                        8345.2 -32711
## - TB             1       0.6  8345.8 -32711
## - PHI            1       0.7  8345.9 -32710
## - TEN            1       0.9  8346.0 -32710
## - MINN           1       1.0  8346.1 -32710
## - ATL            1       1.1  8346.2 -32709
## - NE             1       1.3  8346.4 -32709
## - BAL            1       1.3  8346.5 -32709
## - WAS            1       1.3  8346.5 -32708
## - ARI            1       1.5  8346.7 -32708
## - SD             1       1.6  8346.7 -32708
## - CLE            1       2.3  8347.5 -32705
## - CIN            1       2.6  8347.8 -32704
## - DET            1       2.9  8348.1 -32703
## - HOU            1       3.4  8348.5 -32702
## - STL            1       3.4  8348.6 -32701
## - cold_weather   1       3.5  8348.6 -32701
## - NYG            1       4.1  8349.3 -32699
## - DEN            1       6.4  8351.6 -32692
## - forty1         1      15.6  8360.8 -32661
## - avg_rbry_pos   1      45.3  8390.5 -32564
## - avg_rbry_plyr  1    8575.8 16921.0 -13285
## 
## Step:  AIC=-32711.31
## ra ~ cold_weather + home_team_1 + forty1 + ARI + ATL + BAL + 
##     CIN + CLE + DEN + DET + HOU + MINN + NE + NYG + PHI + SD + 
##     STL + TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## - home_team_1    1       0.4  8346.0 -32712
## - TB             1       0.6  8346.2 -32711
## <none>                        8345.6 -32711
## - PHI            1       0.7  8346.3 -32711
## - TEN            1       0.9  8346.5 -32710
## - MINN           1       1.0  8346.6 -32710
## - ATL            1       1.1  8346.7 -32710
## - NE             1       1.3  8346.9 -32709
## - BAL            1       1.3  8346.9 -32709
## - WAS            1       1.3  8347.0 -32709
## - SD             1       1.5  8347.1 -32708
## - ARI            1       1.5  8347.1 -32708
## - CLE            1       2.3  8347.9 -32706
## - CIN            1       2.6  8348.2 -32705
## - DET            1       3.0  8348.6 -32704
## - STL            1       3.4  8349.0 -32702
## - HOU            1       3.4  8349.0 -32702
## - cold_weather   1       3.5  8349.1 -32702
## - NYG            1       4.1  8349.7 -32700
## - DEN            1       6.4  8352.0 -32692
## - forty1         1      15.7  8361.3 -32662
## - avg_rbry_pos   1      45.4  8391.0 -32564
## - avg_rbry_plyr  1    8575.4 16921.0 -13287
## 
## Step:  AIC=-32711.86
## ra ~ cold_weather + forty1 + ARI + ATL + BAL + CIN + CLE + DEN + 
##     DET + HOU + MINN + NE + NYG + PHI + SD + STL + TB + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos
## 
##                 Df Sum of Sq     RSS    AIC
## <none>                        8346.0 -32712
## - TB             1       0.6  8346.7 -32712
## - PHI            1       0.7  8346.7 -32712
## - TEN            1       0.9  8347.0 -32711
## - ATL            1       0.9  8347.0 -32711
## - MINN           1       1.0  8347.0 -32711
## - NE             1       1.3  8347.4 -32709
## - ARI            1       1.3  8347.4 -32709
## - BAL            1       1.3  8347.4 -32709
## - WAS            1       1.4  8347.5 -32709
## - SD             1       1.5  8347.6 -32709
## - CLE            1       2.4  8348.4 -32706
## - CIN            1       2.7  8348.7 -32705
## - DET            1       2.8  8348.8 -32705
## - STL            1       3.2  8349.2 -32703
## - HOU            1       3.2  8349.2 -32703
## - cold_weather   1       3.8  8349.8 -32701
## - NYG            1       4.2  8350.2 -32700
## - DEN            1       6.5  8352.6 -32692
## - forty1         1      15.6  8361.7 -32662
## - avg_rbry_pos   1      45.4  8391.4 -32565
## - avg_rbry_plyr  1    8575.6 16921.6 -13288

Fumbles

PreProcess:

set.seed(123)
splitfuml <- sample.split(nfl_data$fuml, SplitRatio = 0.7)
Trainfuml <- subset(nfl_data, split == TRUE)
Testfuml <- subset(nfl_data, split == FALSE)
preProcValues <- preProcess(Trainfuml, method = c("center", "scale"))
trainTransformedfuml <- predict(preProcValues, Trainfuml)
testTransformedfuml <- predict(preProcValues, Testfuml)

ggpairs:

ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[1:9]))])

ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[10:18]))])

ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[19:27]))])

ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[28:36]))])

ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[37:45]))])

ggpairs(nfl_data[,c("fuml",colnames(filtered_nfl_data_fields[46:51]))])

fumlregform <- formula(paste("fuml ~ ", 
                           paste(colnames(filtered_nfl_data_fields), collapse="+")))

linRegFumble <- lm(fumlregform, data = trainTransformedfuml)
summary(linRegFumble)
## 
## Call:
## lm(formula = fumlregform, data = trainTransformedfuml)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2702 -0.2647 -0.1117 -0.0102 15.9907 
## 
## Coefficients: (6 not defined because of singularities)
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      2.587e-16  5.750e-03   0.000   1.0000    
## height           4.911e-03  1.116e-02   0.440   0.6598    
## weight           6.203e-04  1.046e-02   0.059   0.9527    
## cold_weather     1.146e-02  6.053e-03   1.893   0.0583 .  
## hot_weather      8.272e-04  5.803e-03   0.143   0.8866    
## home_team_1     -3.380e-03  6.257e-03  -0.540   0.5890    
## forty1          -4.425e-03  9.924e-03  -0.446   0.6556    
## vertical1       -4.639e-03  7.630e-03  -0.608   0.5432    
## ARI             -5.726e-03  8.044e-03  -0.712   0.4766    
## ATL             -3.851e-03  8.082e-03  -0.477   0.6337    
## BAL             -6.381e-03  8.089e-03  -0.789   0.4302    
## BUF             -4.508e-03  7.985e-03  -0.565   0.5724    
## CAR             -5.196e-03  7.933e-03  -0.655   0.5125    
## CHI             -1.287e-02  7.844e-03  -1.641   0.1009    
## CIN             -8.660e-03  7.989e-03  -1.084   0.2784    
## CLE             -3.170e-03  7.952e-03  -0.399   0.6902    
## DAL             -4.528e-03  8.033e-03  -0.564   0.5730    
## DEN             -1.587e-03  8.063e-03  -0.197   0.8440    
## DET             -3.160e-03  7.952e-03  -0.397   0.6911    
## GB              -3.152e-03  8.187e-03  -0.385   0.7002    
## HOU             -1.501e-03  8.089e-03  -0.186   0.8528    
## IND             -1.066e-02  8.030e-03  -1.328   0.1843    
## JAC             -2.399e-03  7.833e-03  -0.306   0.7595    
## KC              -7.052e-04  8.005e-03  -0.088   0.9298    
## MIA             -2.711e-04  7.876e-03  -0.034   0.9725    
## MINN            -3.456e-03  7.924e-03  -0.436   0.6628    
## NE              -1.030e-02  8.276e-03  -1.244   0.2134    
## NOR             -1.055e-02  8.251e-03  -1.279   0.2008    
## NYG              1.798e-03  8.064e-03   0.223   0.8236    
## NYJ             -1.242e-02  8.035e-03  -1.546   0.1220    
## OAK             -6.913e-04  8.085e-03  -0.085   0.9319    
## PHI              1.705e-03  7.835e-03   0.218   0.8278    
## PIT             -5.273e-03  8.040e-03  -0.656   0.5119    
## SD              -9.969e-04  7.890e-03  -0.126   0.8995    
## SEA              9.747e-04  8.189e-03   0.119   0.9053    
## STL             -9.614e-04  7.970e-03  -0.121   0.9040    
## TB              -3.135e-03  7.895e-03  -0.397   0.6913    
## TEN             -7.993e-03  7.943e-03  -1.006   0.3143    
## WAS             -4.065e-03  7.985e-03  -0.509   0.6107    
## avg_trg_team            NA         NA      NA       NA    
## avg_rectd_plyr  -2.112e-03  7.343e-03  -0.288   0.7736    
## avg_tdr_team            NA         NA      NA       NA    
## avg_rbra_team           NA         NA      NA       NA    
## avg_rbry_plyr   -4.601e-03  8.787e-03  -0.524   0.6006    
## avg_rbry_pos     5.521e-03  1.024e-02   0.539   0.5898    
## avg_fuml_plyr    3.088e-01  8.494e-03  36.352   <2e-16 ***
## avg_fuml_team           NA         NA      NA       NA    
## avg_qbints_team         NA         NA      NA       NA    
## avg_qbtdp_plyr  -8.624e-03  9.227e-03  -0.935   0.3499    
## avg_qbtdp_team          NA         NA      NA       NA    
## grass_1         -8.645e-03  6.616e-03  -1.307   0.1913    
## bad_weather_1    1.779e-03  5.850e-03   0.304   0.7610    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9533 on 27438 degrees of freedom
## Multiple R-squared:  0.09271,    Adjusted R-squared:  0.09122 
## F-statistic: 62.31 on 45 and 27438 DF,  p-value: < 2.2e-16
linRegFumble2 <- lm(fuml ~ avg_fuml_plyr, data = trainTransformedfuml)

summary(linRegFumble2)
## 
## Call:
## lm(formula = fuml ~ avg_fuml_plyr, data = trainTransformedfuml)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.2292 -0.2679 -0.1108  0.0000 16.0207 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1.991e-16  5.748e-03    0.00        1    
## avg_fuml_plyr 3.033e-01  5.748e-03   52.76   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9529 on 27482 degrees of freedom
## Multiple R-squared:  0.09197,    Adjusted R-squared:  0.09194 
## F-statistic:  2784 on 1 and 27482 DF,  p-value: < 2.2e-16

Definitely does not seem to be a good predictor

Testing the data, we see that the training set and the test set are similar. The model seems to hold up through testing

FumblePredicted <- predict(linRegFumble2, newdata = testTransformedfuml)

SSEfum <- sum((FumblePredicted - testTransformedfuml$fuml)^2)
SSTfum <- sum((mean(nfl_data$fuml)-testTransformedfuml$fuml)^2)
r2_fum <- 1 - SSEfum/SSTfum 
r2_fum
## [1] 0.08604778
rmse_fum <- sqrt(SSEfum/nrow(testTransformedfuml))
rmse_fum
## [1] 0.9529244

Regression plots:

par(mar = c(4, 4, 2, 2), mfrow = c(2, 2))
plot(linRegFumble2, which = c(1:3,5))

The plots don’t seem to confirm that this is a good model for the data

Summary statistics:

confint(linRegFumble2)
##                     2.5 %     97.5 %
## (Intercept)   -0.01126638 0.01126638
## avg_fuml_plyr  0.29200585 0.31453901
coef(summary(linRegFumble2))
##                   Estimate  Std. Error      t value Pr(>|t|)
## (Intercept)   1.990785e-16 0.005748004 3.463437e-14        1
## avg_fuml_plyr 3.032724e-01 0.005748108 5.276039e+01        0
anova(linRegFumble2)
## Analysis of Variance Table
## 
## Response: fuml
##                  Df  Sum Sq Mean Sq F value    Pr(>F)    
## avg_fuml_plyr     1  2527.7 2527.73  2783.7 < 2.2e-16 ***
## Residuals     27482 24955.3    0.91                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC:

aic_fuml <- step(lm(fumlregform, data = trainTransformedfuml), direction = "backward")
## Start:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     avg_qbtdp_team + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbints_team + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_fuml_team + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
## 
## Step:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbra_team + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_tdr_team + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_trg_team + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
## 
## Step:  AIC=-2583.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MIA + MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + 
##     SEA + STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - MIA             1      0.00 24935 -2585.0
## - weight          1      0.00 24935 -2585.0
## - OAK             1      0.01 24935 -2585.0
## - KC              1      0.01 24935 -2585.0
## - SEA             1      0.01 24935 -2585.0
## - STL             1      0.01 24935 -2585.0
## - SD              1      0.01 24935 -2585.0
## - hot_weather     1      0.02 24935 -2585.0
## - HOU             1      0.03 24935 -2585.0
## - DEN             1      0.04 24935 -2585.0
## - PHI             1      0.04 24935 -2585.0
## - NYG             1      0.05 24935 -2585.0
## - avg_rectd_plyr  1      0.08 24935 -2585.0
## - bad_weather_1   1      0.08 24935 -2584.9
## - JAC             1      0.09 24935 -2584.9
## - GB              1      0.13 24935 -2584.9
## - TB              1      0.14 24935 -2584.9
## - DET             1      0.14 24935 -2584.9
## - CLE             1      0.14 24935 -2584.9
## - MINN            1      0.17 24935 -2584.8
## - height          1      0.18 24935 -2584.8
## - forty1          1      0.18 24935 -2584.8
## - ATL             1      0.21 24935 -2584.8
## - WAS             1      0.24 24935 -2584.8
## - avg_rbry_plyr   1      0.25 24935 -2584.8
## - avg_rbry_pos    1      0.26 24935 -2584.8
## - home_team_1     1      0.27 24935 -2584.8
## - DAL             1      0.29 24935 -2584.7
## - BUF             1      0.29 24935 -2584.7
## - vertical1       1      0.34 24935 -2584.7
## - CAR             1      0.39 24935 -2584.6
## - PIT             1      0.39 24935 -2584.6
## - ARI             1      0.46 24936 -2584.5
## - BAL             1      0.57 24936 -2584.4
## - avg_qbtdp_plyr  1      0.79 24936 -2584.2
## - TEN             1      0.92 24936 -2584.0
## - CIN             1      1.07 24936 -2583.9
## - NE              1      1.41 24936 -2583.5
## - NOR             1      1.49 24937 -2583.4
## - grass_1         1      1.55 24937 -2583.3
## - IND             1      1.60 24937 -2583.3
## <none>                        24935 -2583.0
## - NYJ             1      2.17 24937 -2582.6
## - CHI             1      2.45 24938 -2582.3
## - cold_weather    1      3.26 24938 -2581.4
## - avg_fuml_plyr   1   1200.94 26136 -1292.2
## 
## Step:  AIC=-2585.04
## fuml ~ height + weight + cold_weather + hot_weather + home_team_1 + 
##     forty1 + vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + 
##     CIN + CLE + DAL + DEN + DET + GB + HOU + IND + JAC + KC + 
##     MINN + NE + NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + 
##     STL + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - weight          1      0.00 24935 -2587.0
## - OAK             1      0.01 24935 -2587.0
## - KC              1      0.01 24935 -2587.0
## - STL             1      0.01 24935 -2587.0
## - SD              1      0.01 24935 -2587.0
## - hot_weather     1      0.02 24935 -2587.0
## - SEA             1      0.02 24935 -2587.0
## - HOU             1      0.03 24935 -2587.0
## - DEN             1      0.04 24935 -2587.0
## - PHI             1      0.06 24935 -2587.0
## - NYG             1      0.07 24935 -2587.0
## - avg_rectd_plyr  1      0.08 24935 -2587.0
## - bad_weather_1   1      0.08 24935 -2586.9
## - JAC             1      0.10 24935 -2586.9
## - GB              1      0.16 24935 -2586.9
## - DET             1      0.17 24935 -2586.8
## - TB              1      0.17 24935 -2586.8
## - CLE             1      0.17 24935 -2586.8
## - height          1      0.18 24935 -2586.8
## - forty1          1      0.18 24935 -2586.8
## - MINN            1      0.21 24935 -2586.8
## - avg_rbry_plyr   1      0.25 24935 -2586.8
## - ATL             1      0.25 24935 -2586.8
## - avg_rbry_pos    1      0.26 24935 -2586.8
## - home_team_1     1      0.27 24935 -2586.8
## - WAS             1      0.29 24935 -2586.7
## - vertical1       1      0.33 24935 -2586.7
## - DAL             1      0.35 24935 -2586.7
## - BUF             1      0.35 24935 -2586.7
## - CAR             1      0.48 24936 -2586.5
## - PIT             1      0.49 24936 -2586.5
## - ARI             1      0.57 24936 -2586.4
## - BAL             1      0.71 24936 -2586.2
## - avg_qbtdp_plyr  1      0.79 24936 -2586.2
## - TEN             1      1.16 24936 -2585.8
## - CIN             1      1.35 24936 -2585.6
## - grass_1         1      1.55 24937 -2585.3
## - NE              1      1.79 24937 -2585.1
## <none>                        24935 -2585.0
## - NOR             1      1.91 24937 -2584.9
## - IND             1      2.03 24937 -2584.8
## - NYJ             1      2.77 24938 -2584.0
## - CHI             1      3.11 24938 -2583.6
## - cold_weather    1      3.26 24938 -2583.4
## - avg_fuml_plyr   1   1201.25 26136 -1293.9
## 
## Step:  AIC=-2587.03
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MINN + NE + 
##     NOR + NYG + NYJ + OAK + PHI + PIT + SD + SEA + STL + TB + 
##     TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - OAK             1      0.01 24935 -2589.0
## - KC              1      0.01 24935 -2589.0
## - STL             1      0.01 24935 -2589.0
## - SD              1      0.01 24935 -2589.0
## - hot_weather     1      0.02 24935 -2589.0
## - SEA             1      0.02 24935 -2589.0
## - HOU             1      0.03 24935 -2589.0
## - DEN             1      0.04 24935 -2589.0
## - PHI             1      0.06 24935 -2589.0
## - NYG             1      0.07 24935 -2589.0
## - avg_rectd_plyr  1      0.07 24935 -2588.9
## - bad_weather_1   1      0.08 24935 -2588.9
## - JAC             1      0.10 24935 -2588.9
## - GB              1      0.16 24935 -2588.9
## - DET             1      0.17 24935 -2588.8
## - TB              1      0.17 24935 -2588.8
## - CLE             1      0.17 24935 -2588.8
## - forty1          1      0.19 24935 -2588.8
## - MINN            1      0.21 24935 -2588.8
## - avg_rbry_plyr   1      0.25 24935 -2588.8
## - ATL             1      0.25 24935 -2588.8
## - home_team_1     1      0.27 24935 -2588.7
## - WAS             1      0.29 24935 -2588.7
## - vertical1       1      0.33 24935 -2588.7
## - avg_rbry_pos    1      0.33 24935 -2588.7
## - DAL             1      0.35 24935 -2588.6
## - BUF             1      0.36 24935 -2588.6
## - height          1      0.43 24936 -2588.6
## - CAR             1      0.48 24936 -2588.5
## - PIT             1      0.49 24936 -2588.5
## - ARI             1      0.57 24936 -2588.4
## - BAL             1      0.71 24936 -2588.2
## - avg_qbtdp_plyr  1      0.88 24936 -2588.1
## - TEN             1      1.17 24936 -2587.8
## - CIN             1      1.36 24936 -2587.5
## - grass_1         1      1.55 24937 -2587.3
## - NE              1      1.80 24937 -2587.1
## <none>                        24935 -2587.0
## - NOR             1      1.91 24937 -2586.9
## - IND             1      2.03 24937 -2586.8
## - NYJ             1      2.77 24938 -2586.0
## - CHI             1      3.12 24938 -2585.6
## - cold_weather    1      3.26 24938 -2585.4
## - avg_fuml_plyr   1   1211.40 26146 -1285.2
## 
## Step:  AIC=-2589.03
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + KC + MINN + NE + 
##     NOR + NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + TEN + 
##     WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - KC              1      0.00 24935 -2591.0
## - STL             1      0.01 24935 -2591.0
## - SD              1      0.01 24935 -2591.0
## - hot_weather     1      0.02 24935 -2591.0
## - HOU             1      0.03 24935 -2591.0
## - DEN             1      0.03 24935 -2591.0
## - SEA             1      0.03 24935 -2591.0
## - avg_rectd_plyr  1      0.07 24935 -2590.9
## - bad_weather_1   1      0.08 24935 -2590.9
## - PHI             1      0.09 24935 -2590.9
## - NYG             1      0.09 24935 -2590.9
## - JAC             1      0.09 24935 -2590.9
## - GB              1      0.16 24935 -2590.8
## - DET             1      0.17 24935 -2590.8
## - TB              1      0.17 24935 -2590.8
## - CLE             1      0.17 24935 -2590.8
## - forty1          1      0.19 24935 -2590.8
## - MINN            1      0.21 24935 -2590.8
## - avg_rbry_plyr   1      0.24 24935 -2590.8
## - ATL             1      0.25 24935 -2590.8
## - home_team_1     1      0.26 24935 -2590.7
## - WAS             1      0.29 24935 -2590.7
## - avg_rbry_pos    1      0.33 24935 -2590.7
## - vertical1       1      0.33 24935 -2590.7
## - DAL             1      0.36 24935 -2590.6
## - BUF             1      0.37 24935 -2590.6
## - height          1      0.42 24936 -2590.6
## - CAR             1      0.50 24936 -2590.5
## - PIT             1      0.51 24936 -2590.5
## - ARI             1      0.60 24936 -2590.4
## - BAL             1      0.76 24936 -2590.2
## - avg_qbtdp_plyr  1      0.88 24936 -2590.1
## - TEN             1      1.26 24936 -2589.6
## - CIN             1      1.45 24937 -2589.4
## - grass_1         1      1.56 24937 -2589.3
## <none>                        24935 -2589.0
## - NE              1      1.93 24937 -2588.9
## - NOR             1      2.08 24937 -2588.7
## - IND             1      2.19 24937 -2588.6
## - NYJ             1      3.01 24938 -2587.7
## - cold_weather    1      3.26 24938 -2587.4
## - CHI             1      3.40 24938 -2587.3
## - avg_fuml_plyr   1   1211.79 26147 -1286.8
## 
## Step:  AIC=-2591.02
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + 
##     NYG + NYJ + PHI + PIT + SD + SEA + STL + TB + TEN + WAS + 
##     avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - STL             1      0.01 24935 -2593.0
## - SD              1      0.01 24935 -2593.0
## - hot_weather     1      0.02 24935 -2593.0
## - HOU             1      0.03 24935 -2593.0
## - DEN             1      0.03 24935 -2593.0
## - SEA             1      0.04 24935 -2593.0
## - avg_rectd_plyr  1      0.07 24935 -2592.9
## - bad_weather_1   1      0.08 24935 -2592.9
## - JAC             1      0.09 24935 -2592.9
## - PHI             1      0.10 24935 -2592.9
## - NYG             1      0.11 24935 -2592.9
## - GB              1      0.16 24935 -2592.8
## - DET             1      0.17 24935 -2592.8
## - TB              1      0.17 24935 -2592.8
## - CLE             1      0.17 24935 -2592.8
## - forty1          1      0.19 24935 -2592.8
## - MINN            1      0.21 24935 -2592.8
## - avg_rbry_plyr   1      0.24 24935 -2592.8
## - ATL             1      0.25 24935 -2592.7
## - home_team_1     1      0.26 24935 -2592.7
## - WAS             1      0.30 24935 -2592.7
## - vertical1       1      0.33 24935 -2592.7
## - avg_rbry_pos    1      0.33 24935 -2592.7
## - DAL             1      0.37 24935 -2592.6
## - BUF             1      0.37 24935 -2592.6
## - height          1      0.43 24936 -2592.6
## - CAR             1      0.52 24936 -2592.5
## - PIT             1      0.53 24936 -2592.4
## - ARI             1      0.62 24936 -2592.3
## - BAL             1      0.78 24936 -2592.2
## - avg_qbtdp_plyr  1      0.88 24936 -2592.1
## - TEN             1      1.31 24936 -2591.6
## - CIN             1      1.51 24937 -2591.4
## - grass_1         1      1.57 24937 -2591.3
## <none>                        24935 -2591.0
## - NE              1      2.02 24937 -2590.8
## - NOR             1      2.17 24937 -2590.6
## - IND             1      2.28 24937 -2590.5
## - NYJ             1      3.15 24938 -2589.6
## - cold_weather    1      3.26 24938 -2589.4
## - CHI             1      3.57 24939 -2589.1
## - avg_fuml_plyr   1   1211.80 26147 -1288.8
## 
## Step:  AIC=-2593.02
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + 
##     NYG + NYJ + PHI + PIT + SD + SEA + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - SD              1      0.01 24935 -2595.0
## - hot_weather     1      0.02 24935 -2595.0
## - HOU             1      0.02 24935 -2595.0
## - DEN             1      0.03 24935 -2595.0
## - SEA             1      0.05 24935 -2595.0
## - avg_rectd_plyr  1      0.07 24935 -2594.9
## - JAC             1      0.08 24935 -2594.9
## - bad_weather_1   1      0.09 24935 -2594.9
## - PHI             1      0.12 24935 -2594.9
## - NYG             1      0.12 24935 -2594.9
## - GB              1      0.15 24935 -2594.8
## - DET             1      0.16 24935 -2594.8
## - TB              1      0.16 24935 -2594.8
## - CLE             1      0.16 24935 -2594.8
## - forty1          1      0.19 24935 -2594.8
## - MINN            1      0.20 24935 -2594.8
## - avg_rbry_plyr   1      0.24 24935 -2594.8
## - ATL             1      0.25 24935 -2594.7
## - home_team_1     1      0.26 24935 -2594.7
## - WAS             1      0.29 24935 -2594.7
## - vertical1       1      0.33 24935 -2594.7
## - avg_rbry_pos    1      0.33 24935 -2594.7
## - DAL             1      0.36 24935 -2594.6
## - BUF             1      0.37 24935 -2594.6
## - height          1      0.43 24936 -2594.5
## - CAR             1      0.51 24936 -2594.4
## - PIT             1      0.52 24936 -2594.4
## - ARI             1      0.62 24936 -2594.3
## - BAL             1      0.78 24936 -2594.2
## - avg_qbtdp_plyr  1      0.88 24936 -2594.1
## - TEN             1      1.32 24936 -2593.6
## - CIN             1      1.53 24937 -2593.3
## - grass_1         1      1.57 24937 -2593.3
## <none>                        24935 -2593.0
## - NE              1      2.06 24937 -2592.8
## - NOR             1      2.23 24937 -2592.6
## - IND             1      2.34 24937 -2592.4
## - NYJ             1      3.23 24938 -2591.4
## - cold_weather    1      3.26 24938 -2591.4
## - CHI             1      3.63 24939 -2591.0
## - avg_fuml_plyr   1   1212.23 26147 -1290.3
## 
## Step:  AIC=-2595.01
## fuml ~ height + cold_weather + hot_weather + home_team_1 + forty1 + 
##     vertical1 + ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + 
##     DAL + DEN + DET + GB + HOU + IND + JAC + MINN + NE + NOR + 
##     NYG + NYJ + PHI + PIT + SEA + TB + TEN + WAS + avg_rectd_plyr + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - hot_weather     1      0.02 24935 -2597.0
## - HOU             1      0.02 24935 -2597.0
## - DEN             1      0.02 24935 -2597.0
## - SEA             1      0.06 24935 -2596.9
## - avg_rectd_plyr  1      0.07 24935 -2596.9
## - JAC             1      0.08 24935 -2596.9
## - bad_weather_1   1      0.09 24935 -2596.9
## - PHI             1      0.13 24935 -2596.9
## - NYG             1      0.14 24935 -2596.9
## - GB              1      0.15 24935 -2596.8
## - DET             1      0.15 24935 -2596.8
## - TB              1      0.16 24935 -2596.8
## - CLE             1      0.16 24935 -2596.8
## - forty1          1      0.19 24935 -2596.8
## - MINN            1      0.20 24935 -2596.8
## - ATL             1      0.24 24935 -2596.7
## - avg_rbry_plyr   1      0.24 24935 -2596.7
## - home_team_1     1      0.26 24935 -2596.7
## - WAS             1      0.28 24935 -2596.7
## - vertical1       1      0.33 24935 -2596.7
## - avg_rbry_pos    1      0.33 24935 -2596.7
## - DAL             1      0.36 24935 -2596.6
## - BUF             1      0.36 24935 -2596.6
## - height          1      0.43 24936 -2596.5
## - CAR             1      0.51 24936 -2596.4
## - PIT             1      0.52 24936 -2596.4
## - ARI             1      0.61 24936 -2596.3
## - BAL             1      0.78 24936 -2596.2
## - avg_qbtdp_plyr  1      0.88 24936 -2596.0
## - TEN             1      1.32 24936 -2595.6
## - CIN             1      1.54 24937 -2595.3
## - grass_1         1      1.58 24937 -2595.3
## <none>                        24935 -2595.0
## - NE              1      2.08 24937 -2594.7
## - NOR             1      2.25 24937 -2594.5
## - IND             1      2.36 24937 -2594.4
## - cold_weather    1      3.27 24938 -2593.4
## - NYJ             1      3.27 24938 -2593.4
## - CHI             1      3.67 24939 -2593.0
## - avg_fuml_plyr   1   1212.24 26147 -1292.3
## 
## Step:  AIC=-2596.99
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + HOU + IND + JAC + MINN + NE + NOR + NYG + NYJ + 
##     PHI + PIT + SEA + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - HOU             1      0.02 24935 -2599.0
## - DEN             1      0.02 24935 -2599.0
## - SEA             1      0.06 24935 -2598.9
## - avg_rectd_plyr  1      0.07 24935 -2598.9
## - JAC             1      0.08 24935 -2598.9
## - bad_weather_1   1      0.09 24935 -2598.9
## - PHI             1      0.13 24935 -2598.8
## - NYG             1      0.14 24935 -2598.8
## - GB              1      0.15 24935 -2598.8
## - TB              1      0.15 24935 -2598.8
## - DET             1      0.16 24935 -2598.8
## - CLE             1      0.16 24935 -2598.8
## - forty1          1      0.19 24935 -2598.8
## - MINN            1      0.20 24935 -2598.8
## - avg_rbry_plyr   1      0.24 24935 -2598.7
## - ATL             1      0.24 24935 -2598.7
## - home_team_1     1      0.26 24935 -2598.7
## - WAS             1      0.29 24935 -2598.7
## - vertical1       1      0.33 24935 -2598.6
## - avg_rbry_pos    1      0.33 24935 -2598.6
## - BUF             1      0.36 24935 -2598.6
## - DAL             1      0.36 24935 -2598.6
## - height          1      0.43 24936 -2598.5
## - CAR             1      0.51 24936 -2598.4
## - PIT             1      0.52 24936 -2598.4
## - ARI             1      0.61 24936 -2598.3
## - BAL             1      0.78 24936 -2598.1
## - avg_qbtdp_plyr  1      0.88 24936 -2598.0
## - TEN             1      1.33 24936 -2597.5
## - CIN             1      1.54 24937 -2597.3
## - grass_1         1      1.57 24937 -2597.3
## <none>                        24935 -2597.0
## - NE              1      2.08 24937 -2596.7
## - NOR             1      2.25 24937 -2596.5
## - IND             1      2.36 24937 -2596.4
## - cold_weather    1      3.25 24938 -2595.4
## - NYJ             1      3.26 24938 -2595.4
## - CHI             1      3.68 24939 -2594.9
## - avg_fuml_plyr   1   1212.29 26147 -1294.2
## 
## Step:  AIC=-2598.97
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DEN + 
##     DET + GB + IND + JAC + MINN + NE + NOR + NYG + NYJ + PHI + 
##     PIT + SEA + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + 
##     bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - DEN             1      0.02 24935 -2600.9
## - JAC             1      0.07 24935 -2600.9
## - avg_rectd_plyr  1      0.07 24935 -2600.9
## - SEA             1      0.08 24935 -2600.9
## - bad_weather_1   1      0.08 24935 -2600.9
## - GB              1      0.14 24935 -2600.8
## - DET             1      0.14 24935 -2600.8
## - PHI             1      0.14 24935 -2600.8
## - TB              1      0.14 24935 -2600.8
## - CLE             1      0.15 24935 -2600.8
## - NYG             1      0.16 24935 -2600.8
## - MINN            1      0.18 24935 -2600.8
## - forty1          1      0.20 24935 -2600.8
## - ATL             1      0.23 24935 -2600.7
## - avg_rbry_plyr   1      0.25 24935 -2600.7
## - home_team_1     1      0.25 24935 -2600.7
## - WAS             1      0.27 24935 -2600.7
## - avg_rbry_pos    1      0.33 24935 -2600.6
## - vertical1       1      0.34 24935 -2600.6
## - BUF             1      0.34 24935 -2600.6
## - DAL             1      0.34 24935 -2600.6
## - height          1      0.43 24936 -2600.5
## - CAR             1      0.49 24936 -2600.4
## - PIT             1      0.50 24936 -2600.4
## - ARI             1      0.60 24936 -2600.3
## - BAL             1      0.77 24936 -2600.1
## - avg_qbtdp_plyr  1      0.88 24936 -2600.0
## - TEN             1      1.31 24936 -2599.5
## - CIN             1      1.52 24937 -2599.3
## - grass_1         1      1.55 24937 -2599.3
## <none>                        24935 -2599.0
## - NE              1      2.07 24937 -2598.7
## - NOR             1      2.24 24937 -2598.5
## - IND             1      2.36 24937 -2598.4
## - NYJ             1      3.26 24938 -2597.4
## - cold_weather    1      3.27 24938 -2597.4
## - CHI             1      3.68 24939 -2596.9
## - avg_fuml_plyr   1   1213.13 26148 -1295.3
## 
## Step:  AIC=-2600.95
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET + 
##     GB + IND + JAC + MINN + NE + NOR + NYG + NYJ + PHI + PIT + 
##     SEA + TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - JAC             1      0.06 24935 -2602.9
## - avg_rectd_plyr  1      0.08 24935 -2602.9
## - bad_weather_1   1      0.09 24935 -2602.9
## - SEA             1      0.09 24935 -2602.9
## - GB              1      0.13 24935 -2602.8
## - TB              1      0.13 24935 -2602.8
## - DET             1      0.13 24935 -2602.8
## - CLE             1      0.14 24935 -2602.8
## - PHI             1      0.16 24935 -2602.8
## - MINN            1      0.17 24935 -2602.8
## - NYG             1      0.17 24935 -2602.8
## - forty1          1      0.20 24935 -2602.7
## - ATL             1      0.22 24935 -2602.7
## - avg_rbry_plyr   1      0.25 24935 -2602.7
## - home_team_1     1      0.26 24935 -2602.7
## - WAS             1      0.26 24935 -2602.7
## - BUF             1      0.33 24935 -2602.6
## - DAL             1      0.33 24935 -2602.6
## - avg_rbry_pos    1      0.33 24935 -2602.6
## - vertical1       1      0.35 24935 -2602.6
## - height          1      0.44 24936 -2602.5
## - CAR             1      0.48 24936 -2602.4
## - PIT             1      0.48 24936 -2602.4
## - ARI             1      0.58 24936 -2602.3
## - BAL             1      0.75 24936 -2602.1
## - avg_qbtdp_plyr  1      0.88 24936 -2602.0
## - TEN             1      1.29 24936 -2601.5
## - CIN             1      1.51 24937 -2601.3
## - grass_1         1      1.57 24937 -2601.2
## <none>                        24935 -2600.9
## - NE              1      2.05 24937 -2600.7
## - NOR             1      2.23 24937 -2600.5
## - IND             1      2.34 24937 -2600.4
## - cold_weather    1      3.25 24938 -2599.4
## - NYJ             1      3.25 24938 -2599.4
## - CHI             1      3.67 24939 -2598.9
## - avg_fuml_plyr   1   1213.27 26148 -1297.2
## 
## Step:  AIC=-2602.88
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET + 
##     GB + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + 
##     TB + TEN + WAS + avg_rectd_plyr + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_rectd_plyr  1      0.08 24935 -2604.8
## - bad_weather_1   1      0.09 24935 -2604.8
## - SEA             1      0.11 24935 -2604.8
## - GB              1      0.11 24935 -2604.8
## - TB              1      0.11 24935 -2604.8
## - DET             1      0.12 24935 -2604.8
## - CLE             1      0.12 24935 -2604.8
## - MINN            1      0.15 24935 -2604.7
## - PHI             1      0.18 24935 -2604.7
## - ATL             1      0.20 24935 -2604.7
## - NYG             1      0.20 24935 -2604.7
## - forty1          1      0.21 24935 -2604.7
## - WAS             1      0.23 24935 -2604.6
## - avg_rbry_plyr   1      0.25 24935 -2604.6
## - home_team_1     1      0.26 24935 -2604.6
## - BUF             1      0.30 24936 -2604.6
## - DAL             1      0.30 24936 -2604.6
## - avg_rbry_pos    1      0.34 24936 -2604.5
## - vertical1       1      0.37 24936 -2604.5
## - height          1      0.45 24936 -2604.4
## - CAR             1      0.45 24936 -2604.4
## - PIT             1      0.45 24936 -2604.4
## - ARI             1      0.55 24936 -2604.3
## - BAL             1      0.71 24936 -2604.1
## - avg_qbtdp_plyr  1      0.89 24936 -2603.9
## - TEN             1      1.25 24936 -2603.5
## - CIN             1      1.46 24937 -2603.3
## - grass_1         1      1.58 24937 -2603.1
## <none>                        24935 -2602.9
## - NE              1      2.00 24937 -2602.7
## - NOR             1      2.17 24937 -2602.5
## - IND             1      2.29 24938 -2602.4
## - NYJ             1      3.19 24938 -2601.4
## - cold_weather    1      3.28 24938 -2601.3
## - CHI             1      3.61 24939 -2600.9
## - avg_fuml_plyr   1   1213.63 26149 -1298.7
## 
## Step:  AIC=-2604.8
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET + 
##     GB + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + 
##     TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1 + bad_weather_1
## 
##                  Df Sum of Sq   RSS     AIC
## - bad_weather_1   1      0.09 24935 -2606.7
## - SEA             1      0.10 24935 -2606.7
## - CLE             1      0.11 24935 -2606.7
## - TB              1      0.11 24935 -2606.7
## - DET             1      0.13 24935 -2606.7
## - GB              1      0.13 24935 -2606.7
## - MINN            1      0.14 24935 -2606.6
## - PHI             1      0.18 24935 -2606.6
## - forty1          1      0.19 24935 -2606.6
## - NYG             1      0.19 24935 -2606.6
## - ATL             1      0.21 24936 -2606.6
## - WAS             1      0.23 24936 -2606.5
## - avg_rbry_plyr   1      0.25 24936 -2606.5
## - home_team_1     1      0.27 24936 -2606.5
## - BUF             1      0.30 24936 -2606.5
## - DAL             1      0.32 24936 -2606.4
## - vertical1       1      0.39 24936 -2606.4
## - height          1      0.40 24936 -2606.4
## - CAR             1      0.44 24936 -2606.3
## - PIT             1      0.46 24936 -2606.3
## - avg_rbry_pos    1      0.50 24936 -2606.2
## - ARI             1      0.54 24936 -2606.2
## - BAL             1      0.71 24936 -2606.0
## - avg_qbtdp_plyr  1      0.82 24936 -2605.9
## - TEN             1      1.23 24937 -2605.4
## - CIN             1      1.46 24937 -2605.2
## - grass_1         1      1.59 24937 -2605.0
## <none>                        24935 -2604.8
## - NE              1      2.15 24937 -2604.4
## - NOR             1      2.28 24938 -2604.3
## - IND             1      2.31 24938 -2604.2
## - NYJ             1      3.18 24938 -2603.3
## - cold_weather    1      3.29 24939 -2603.2
## - CHI             1      3.60 24939 -2602.8
## - avg_fuml_plyr   1   1214.04 26149 -1300.2
## 
## Step:  AIC=-2606.7
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + CLE + DAL + DET + 
##     GB + IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + 
##     TB + TEN + WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - CLE             1      0.10 24935 -2608.6
## - SEA             1      0.11 24935 -2608.6
## - TB              1      0.12 24935 -2608.6
## - DET             1      0.12 24936 -2608.6
## - GB              1      0.13 24936 -2608.6
## - MINN            1      0.14 24936 -2608.6
## - PHI             1      0.18 24936 -2608.5
## - forty1          1      0.18 24936 -2608.5
## - NYG             1      0.20 24936 -2608.5
## - ATL             1      0.21 24936 -2608.5
## - WAS             1      0.23 24936 -2608.4
## - avg_rbry_plyr   1      0.25 24936 -2608.4
## - home_team_1     1      0.26 24936 -2608.4
## - BUF             1      0.29 24936 -2608.4
## - DAL             1      0.32 24936 -2608.3
## - vertical1       1      0.39 24936 -2608.3
## - height          1      0.40 24936 -2608.3
## - CAR             1      0.44 24936 -2608.2
## - PIT             1      0.46 24936 -2608.2
## - avg_rbry_pos    1      0.50 24936 -2608.2
## - ARI             1      0.54 24936 -2608.1
## - BAL             1      0.71 24936 -2607.9
## - avg_qbtdp_plyr  1      0.81 24936 -2607.8
## - TEN             1      1.24 24937 -2607.3
## - CIN             1      1.45 24937 -2607.1
## - grass_1         1      1.57 24937 -2607.0
## <none>                        24935 -2606.7
## - NE              1      2.12 24937 -2606.4
## - NOR             1      2.27 24938 -2606.2
## - IND             1      2.31 24938 -2606.2
## - NYJ             1      3.17 24939 -2605.2
## - cold_weather    1      3.49 24939 -2604.9
## - CHI             1      3.56 24939 -2604.8
## - avg_fuml_plyr   1   1213.96 26149 -1302.2
## 
## Step:  AIC=-2608.59
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + DET + GB + 
##     IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + TB + 
##     TEN + WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - TB              1      0.10 24936 -2610.5
## - GB              1      0.10 24936 -2610.5
## - DET             1      0.11 24936 -2610.5
## - MINN            1      0.12 24936 -2610.5
## - SEA             1      0.13 24936 -2610.4
## - forty1          1      0.19 24936 -2610.4
## - ATL             1      0.19 24936 -2610.4
## - WAS             1      0.20 24936 -2610.4
## - PHI             1      0.21 24936 -2610.4
## - NYG             1      0.23 24936 -2610.3
## - avg_rbry_plyr   1      0.25 24936 -2610.3
## - BUF             1      0.26 24936 -2610.3
## - home_team_1     1      0.27 24936 -2610.3
## - DAL             1      0.29 24936 -2610.3
## - vertical1       1      0.40 24936 -2610.2
## - CAR             1      0.40 24936 -2610.2
## - height          1      0.41 24936 -2610.1
## - PIT             1      0.41 24936 -2610.1
## - ARI             1      0.50 24936 -2610.0
## - avg_rbry_pos    1      0.51 24936 -2610.0
## - BAL             1      0.67 24936 -2609.8
## - avg_qbtdp_plyr  1      0.80 24936 -2609.7
## - TEN             1      1.18 24937 -2609.3
## - CIN             1      1.39 24937 -2609.1
## - grass_1         1      1.59 24937 -2608.8
## <none>                        24935 -2608.6
## - NE              1      2.05 24938 -2608.3
## - NOR             1      2.20 24938 -2608.2
## - IND             1      2.24 24938 -2608.1
## - NYJ             1      3.09 24939 -2607.2
## - cold_weather    1      3.41 24939 -2606.8
## - CHI             1      3.48 24939 -2606.8
## - avg_fuml_plyr   1   1214.82 26150 -1303.2
## 
## Step:  AIC=-2610.48
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + DET + GB + 
##     IND + MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + TEN + 
##     WAS + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - GB              1      0.09 24936 -2612.4
## - DET             1      0.09 24936 -2612.4
## - MINN            1      0.10 24936 -2612.4
## - SEA             1      0.15 24936 -2612.3
## - ATL             1      0.17 24936 -2612.3
## - WAS             1      0.18 24936 -2612.3
## - forty1          1      0.19 24936 -2612.3
## - PHI             1      0.23 24936 -2612.2
## - BUF             1      0.24 24936 -2612.2
## - avg_rbry_plyr   1      0.25 24936 -2612.2
## - NYG             1      0.26 24936 -2612.2
## - DAL             1      0.26 24936 -2612.2
## - home_team_1     1      0.28 24936 -2612.2
## - CAR             1      0.37 24936 -2612.1
## - PIT             1      0.38 24936 -2612.1
## - vertical1       1      0.39 24936 -2612.1
## - height          1      0.40 24936 -2612.0
## - ARI             1      0.47 24936 -2612.0
## - avg_rbry_pos    1      0.51 24936 -2611.9
## - BAL             1      0.63 24936 -2611.8
## - avg_qbtdp_plyr  1      0.79 24936 -2611.6
## - TEN             1      1.13 24937 -2611.2
## - CIN             1      1.33 24937 -2611.0
## - grass_1         1      1.60 24937 -2610.7
## <none>                        24936 -2610.5
## - NE              1      1.99 24938 -2610.3
## - NOR             1      2.14 24938 -2610.1
## - IND             1      2.18 24938 -2610.1
## - NYJ             1      3.01 24939 -2609.2
## - CHI             1      3.40 24939 -2608.7
## - cold_weather    1      3.47 24939 -2608.7
## - avg_fuml_plyr   1   1214.75 26150 -1305.2
## 
## Step:  AIC=-2612.39
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + DET + IND + 
##     MINN + NE + NOR + NYG + NYJ + PHI + PIT + SEA + TEN + WAS + 
##     avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - DET             1      0.08 24936 -2614.3
## - MINN            1      0.09 24936 -2614.3
## - ATL             1      0.15 24936 -2614.2
## - WAS             1      0.16 24936 -2614.2
## - SEA             1      0.18 24936 -2614.2
## - forty1          1      0.19 24936 -2614.2
## - BUF             1      0.22 24936 -2614.2
## - DAL             1      0.24 24936 -2614.1
## - avg_rbry_plyr   1      0.25 24936 -2614.1
## - PHI             1      0.26 24936 -2614.1
## - NYG             1      0.29 24936 -2614.1
## - home_team_1     1      0.29 24936 -2614.1
## - CAR             1      0.34 24936 -2614.0
## - PIT             1      0.35 24936 -2614.0
## - vertical1       1      0.38 24936 -2614.0
## - height          1      0.41 24936 -2613.9
## - ARI             1      0.44 24936 -2613.9
## - avg_rbry_pos    1      0.52 24936 -2613.8
## - BAL             1      0.59 24936 -2613.7
## - avg_qbtdp_plyr  1      0.82 24936 -2613.5
## - TEN             1      1.09 24937 -2613.2
## - CIN             1      1.28 24937 -2613.0
## - grass_1         1      1.60 24937 -2612.6
## <none>                        24936 -2612.4
## - NE              1      1.92 24938 -2612.3
## - NOR             1      2.08 24938 -2612.1
## - IND             1      2.12 24938 -2612.1
## - NYJ             1      2.95 24939 -2611.1
## - CHI             1      3.33 24939 -2610.7
## - cold_weather    1      3.40 24939 -2610.6
## - avg_fuml_plyr   1   1218.18 26154 -1303.5
## 
## Step:  AIC=-2614.3
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + IND + MINN + 
##     NE + NOR + NYG + NYJ + PHI + PIT + SEA + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - MINN            1      0.08 24936 -2616.2
## - ATL             1      0.13 24936 -2616.2
## - WAS             1      0.14 24936 -2616.2
## - forty1          1      0.19 24936 -2616.1
## - BUF             1      0.19 24936 -2616.1
## - SEA             1      0.20 24936 -2616.1
## - DAL             1      0.22 24936 -2616.1
## - avg_rbry_plyr   1      0.25 24936 -2616.0
## - home_team_1     1      0.27 24936 -2616.0
## - PHI             1      0.28 24936 -2616.0
## - NYG             1      0.32 24936 -2615.9
## - CAR             1      0.32 24936 -2615.9
## - PIT             1      0.33 24936 -2615.9
## - vertical1       1      0.39 24936 -2615.9
## - height          1      0.41 24936 -2615.8
## - ARI             1      0.41 24936 -2615.8
## - avg_rbry_pos    1      0.51 24936 -2615.7
## - BAL             1      0.56 24936 -2615.7
## - avg_qbtdp_plyr  1      0.82 24937 -2615.4
## - TEN             1      1.05 24937 -2615.1
## - CIN             1      1.24 24937 -2614.9
## - grass_1         1      1.54 24937 -2614.6
## <none>                        24936 -2614.3
## - NE              1      1.87 24938 -2614.2
## - NOR             1      2.02 24938 -2614.1
## - IND             1      2.06 24938 -2614.0
## - NYJ             1      2.89 24939 -2613.1
## - CHI             1      3.28 24939 -2612.7
## - cold_weather    1      3.44 24939 -2612.5
## - avg_fuml_plyr   1   1218.29 26154 -1305.3
## 
## Step:  AIC=-2616.22
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + ATL + BAL + BUF + CAR + CHI + CIN + DAL + IND + NE + 
##     NOR + NYG + NYJ + PHI + PIT + SEA + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - ATL             1      0.12 24936 -2618.1
## - WAS             1      0.13 24936 -2618.1
## - BUF             1      0.18 24936 -2618.0
## - forty1          1      0.19 24936 -2618.0
## - DAL             1      0.20 24936 -2618.0
## - SEA             1      0.23 24936 -2618.0
## - avg_rbry_plyr   1      0.26 24936 -2617.9
## - home_team_1     1      0.28 24936 -2617.9
## - CAR             1      0.30 24936 -2617.9
## - PHI             1      0.30 24936 -2617.9
## - PIT             1      0.31 24936 -2617.9
## - NYG             1      0.35 24936 -2617.8
## - ARI             1      0.38 24936 -2617.8
## - height          1      0.40 24936 -2617.8
## - vertical1       1      0.40 24936 -2617.8
## - avg_rbry_pos    1      0.51 24936 -2617.7
## - BAL             1      0.53 24936 -2617.6
## - avg_qbtdp_plyr  1      0.82 24937 -2617.3
## - TEN             1      1.02 24937 -2617.1
## - CIN             1      1.19 24937 -2616.9
## - grass_1         1      1.48 24937 -2616.6
## <none>                        24936 -2616.2
## - NE              1      1.82 24938 -2616.2
## - NOR             1      1.96 24938 -2616.1
## - IND             1      2.01 24938 -2616.0
## - NYJ             1      2.83 24939 -2615.1
## - CHI             1      3.23 24939 -2614.7
## - cold_weather    1      3.42 24939 -2614.4
## - avg_fuml_plyr   1   1218.34 26154 -1307.1
## 
## Step:  AIC=-2618.09
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + BAL + BUF + CAR + CHI + CIN + DAL + IND + NE + NOR + 
##     NYG + NYJ + PHI + PIT + SEA + TEN + WAS + avg_rbry_plyr + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - WAS             1      0.12 24936 -2620.0
## - BUF             1      0.16 24936 -2619.9
## - DAL             1      0.17 24936 -2619.9
## - forty1          1      0.19 24936 -2619.9
## - home_team_1     1      0.24 24936 -2619.8
## - SEA             1      0.25 24936 -2619.8
## - avg_rbry_plyr   1      0.26 24936 -2619.8
## - CAR             1      0.28 24936 -2619.8
## - PIT             1      0.29 24936 -2619.8
## - PHI             1      0.32 24936 -2619.7
## - ARI             1      0.35 24936 -2619.7
## - NYG             1      0.38 24936 -2619.7
## - vertical1       1      0.38 24936 -2619.7
## - height          1      0.42 24936 -2619.6
## - BAL             1      0.49 24936 -2619.5
## - avg_rbry_pos    1      0.52 24936 -2619.5
## - avg_qbtdp_plyr  1      0.84 24937 -2619.2
## - TEN             1      0.99 24937 -2619.0
## - CIN             1      1.15 24937 -2618.8
## - grass_1         1      1.41 24937 -2618.5
## - NE              1      1.75 24938 -2618.2
## <none>                        24936 -2618.1
## - NOR             1      1.89 24938 -2618.0
## - IND             1      1.94 24938 -2617.9
## - NYJ             1      2.76 24939 -2617.1
## - CHI             1      3.18 24939 -2616.6
## - cold_weather    1      3.49 24939 -2616.2
## - avg_fuml_plyr   1   1222.16 26158 -1305.0
## 
## Step:  AIC=-2619.96
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + BAL + BUF + CAR + CHI + CIN + DAL + IND + NE + NOR + 
##     NYG + NYJ + PHI + PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - BUF             1      0.14 24936 -2621.8
## - DAL             1      0.16 24936 -2621.8
## - forty1          1      0.18 24936 -2621.8
## - avg_rbry_plyr   1      0.25 24936 -2621.7
## - home_team_1     1      0.25 24936 -2621.7
## - CAR             1      0.26 24936 -2621.7
## - PIT             1      0.27 24936 -2621.7
## - SEA             1      0.28 24936 -2621.7
## - ARI             1      0.33 24936 -2621.6
## - PHI             1      0.35 24936 -2621.6
## - vertical1       1      0.38 24936 -2621.5
## - NYG             1      0.40 24936 -2621.5
## - height          1      0.44 24936 -2621.5
## - BAL             1      0.47 24937 -2621.4
## - avg_rbry_pos    1      0.53 24937 -2621.4
## - avg_qbtdp_plyr  1      0.85 24937 -2621.0
## - TEN             1      0.94 24937 -2620.9
## - CIN             1      1.11 24937 -2620.7
## - grass_1         1      1.44 24937 -2620.4
## - NE              1      1.71 24938 -2620.1
## <none>                        24936 -2620.0
## - NOR             1      1.84 24938 -2619.9
## - IND             1      1.89 24938 -2619.9
## - NYJ             1      2.70 24939 -2619.0
## - CHI             1      3.11 24939 -2618.5
## - cold_weather    1      3.47 24940 -2618.1
## - avg_fuml_plyr   1   1222.52 26159 -1306.5
## 
## Step:  AIC=-2621.81
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + BAL + CAR + CHI + CIN + DAL + IND + NE + NOR + NYG + 
##     NYJ + PHI + PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - DAL             1      0.14 24936 -2623.7
## - forty1          1      0.16 24936 -2623.6
## - CAR             1      0.24 24936 -2623.5
## - PIT             1      0.25 24936 -2623.5
## - avg_rbry_plyr   1      0.25 24936 -2623.5
## - home_team_1     1      0.27 24936 -2623.5
## - ARI             1      0.30 24936 -2623.5
## - SEA             1      0.31 24937 -2623.5
## - vertical1       1      0.36 24937 -2623.4
## - PHI             1      0.38 24937 -2623.4
## - height          1      0.42 24937 -2623.3
## - BAL             1      0.43 24937 -2623.3
## - NYG             1      0.45 24937 -2623.3
## - avg_rbry_pos    1      0.52 24937 -2623.2
## - avg_qbtdp_plyr  1      0.84 24937 -2622.9
## - TEN             1      0.91 24937 -2622.8
## - CIN             1      1.05 24937 -2622.7
## - grass_1         1      1.35 24938 -2622.3
## - NE              1      1.64 24938 -2622.0
## - NOR             1      1.78 24938 -2621.8
## <none>                        24936 -2621.8
## - IND             1      1.83 24938 -2621.8
## - NYJ             1      2.62 24939 -2620.9
## - CHI             1      3.04 24939 -2620.4
## - cold_weather    1      3.40 24940 -2620.1
## - avg_fuml_plyr   1   1222.44 26159 -1308.5
## 
## Step:  AIC=-2623.65
## fuml ~ height + cold_weather + home_team_1 + forty1 + vertical1 + 
##     ARI + BAL + CAR + CHI + CIN + IND + NE + NOR + NYG + NYJ + 
##     PHI + PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - forty1          1      0.16 24936 -2625.5
## - CAR             1      0.22 24937 -2625.4
## - PIT             1      0.23 24937 -2625.4
## - home_team_1     1      0.24 24937 -2625.4
## - avg_rbry_plyr   1      0.26 24937 -2625.4
## - ARI             1      0.27 24937 -2625.4
## - SEA             1      0.34 24937 -2625.3
## - vertical1       1      0.36 24937 -2625.3
## - PHI             1      0.40 24937 -2625.2
## - BAL             1      0.41 24937 -2625.2
## - height          1      0.42 24937 -2625.2
## - NYG             1      0.48 24937 -2625.1
## - avg_rbry_pos    1      0.53 24937 -2625.1
## - avg_qbtdp_plyr  1      0.85 24937 -2624.7
## - TEN             1      0.88 24937 -2624.7
## - CIN             1      1.01 24937 -2624.5
## - grass_1         1      1.28 24938 -2624.2
## - NE              1      1.59 24938 -2623.9
## - NOR             1      1.72 24938 -2623.8
## - IND             1      1.76 24938 -2623.7
## <none>                        24936 -2623.7
## - NYJ             1      2.56 24939 -2622.8
## - CHI             1      2.99 24939 -2622.3
## - cold_weather    1      3.43 24940 -2621.9
## - avg_fuml_plyr   1   1222.72 26159 -1310.0
## 
## Step:  AIC=-2625.48
## fuml ~ height + cold_weather + home_team_1 + vertical1 + ARI + 
##     BAL + CAR + CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI + 
##     PIT + SEA + TEN + avg_rbry_plyr + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_rbry_plyr   1      0.20 24937 -2627.3
## - vertical1       1      0.21 24937 -2627.2
## - CAR             1      0.22 24937 -2627.2
## - PIT             1      0.23 24937 -2627.2
## - home_team_1     1      0.23 24937 -2627.2
## - ARI             1      0.25 24937 -2627.2
## - height          1      0.28 24937 -2627.2
## - SEA             1      0.35 24937 -2627.1
## - BAL             1      0.41 24937 -2627.0
## - PHI             1      0.41 24937 -2627.0
## - avg_rbry_pos    1      0.44 24937 -2627.0
## - NYG             1      0.47 24937 -2627.0
## - TEN             1      0.88 24937 -2626.5
## - CIN             1      1.01 24937 -2626.4
## - avg_qbtdp_plyr  1      1.10 24938 -2626.3
## - grass_1         1      1.27 24938 -2626.1
## - NOR             1      1.69 24938 -2625.6
## - NE              1      1.70 24938 -2625.6
## - IND             1      1.77 24938 -2625.5
## <none>                        24936 -2625.5
## - NYJ             1      2.60 24939 -2624.6
## - CHI             1      2.95 24939 -2624.2
## - cold_weather    1      3.42 24940 -2623.7
## - avg_fuml_plyr   1   1225.11 26162 -1309.3
## 
## Step:  AIC=-2627.26
## fuml ~ height + cold_weather + home_team_1 + vertical1 + ARI + 
##     BAL + CAR + CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI + 
##     PIT + SEA + TEN + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - vertical1       1      0.23 24937 -2629.0
## - CAR             1      0.23 24937 -2629.0
## - home_team_1     1      0.23 24937 -2629.0
## - PIT             1      0.23 24937 -2629.0
## - avg_rbry_pos    1      0.24 24937 -2629.0
## - ARI             1      0.24 24937 -2629.0
## - height          1      0.28 24937 -2628.9
## - SEA             1      0.33 24937 -2628.9
## - PHI             1      0.40 24937 -2628.8
## - BAL             1      0.40 24937 -2628.8
## - NYG             1      0.48 24937 -2628.7
## - TEN             1      0.88 24938 -2628.3
## - avg_qbtdp_plyr  1      0.96 24938 -2628.2
## - CIN             1      1.03 24938 -2628.1
## - grass_1         1      1.27 24938 -2627.9
## - NOR             1      1.67 24938 -2627.4
## - NE              1      1.73 24938 -2627.3
## - IND             1      1.77 24938 -2627.3
## <none>                        24937 -2627.3
## - NYJ             1      2.62 24939 -2626.4
## - CHI             1      2.97 24940 -2626.0
## - cold_weather    1      3.42 24940 -2625.5
## - avg_fuml_plyr   1   1371.11 26308 -1158.2
## 
## Step:  AIC=-2629.01
## fuml ~ height + cold_weather + home_team_1 + ARI + BAL + CAR + 
##     CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI + PIT + SEA + 
##     TEN + avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - PIT             1      0.23 24937 -2630.8
## - home_team_1     1      0.24 24937 -2630.7
## - ARI             1      0.24 24937 -2630.7
## - CAR             1      0.24 24937 -2630.7
## - SEA             1      0.31 24937 -2630.7
## - avg_rbry_pos    1      0.33 24937 -2630.7
## - height          1      0.38 24937 -2630.6
## - BAL             1      0.40 24937 -2630.6
## - PHI             1      0.41 24937 -2630.6
## - NYG             1      0.49 24937 -2630.5
## - avg_qbtdp_plyr  1      0.79 24938 -2630.1
## - TEN             1      0.89 24938 -2630.0
## - CIN             1      1.01 24938 -2629.9
## - grass_1         1      1.28 24938 -2629.6
## - NE              1      1.66 24939 -2629.2
## - NOR             1      1.71 24939 -2629.1
## <none>                        24937 -2629.0
## - IND             1      1.82 24939 -2629.0
## - NYJ             1      2.71 24940 -2628.0
## - CHI             1      2.94 24940 -2627.8
## - cold_weather    1      3.41 24940 -2627.2
## - avg_fuml_plyr   1   1370.93 26308 -1160.1
## 
## Step:  AIC=-2630.75
## fuml ~ height + cold_weather + home_team_1 + ARI + BAL + CAR + 
##     CHI + CIN + IND + NE + NOR + NYG + NYJ + PHI + SEA + TEN + 
##     avg_rbry_pos + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - CAR             1      0.22 24937 -2632.5
## - ARI             1      0.22 24937 -2632.5
## - home_team_1     1      0.25 24937 -2632.5
## - avg_rbry_pos    1      0.33 24937 -2632.4
## - SEA             1      0.34 24937 -2632.4
## - BAL             1      0.37 24938 -2632.3
## - height          1      0.38 24938 -2632.3
## - PHI             1      0.45 24938 -2632.2
## - NYG             1      0.53 24938 -2632.2
## - avg_qbtdp_plyr  1      0.79 24938 -2631.9
## - TEN             1      0.84 24938 -2631.8
## - CIN             1      0.97 24938 -2631.7
## - grass_1         1      1.35 24938 -2631.3
## - NE              1      1.59 24939 -2631.0
## - NOR             1      1.66 24939 -2630.9
## - IND             1      1.77 24939 -2630.8
## <none>                        24937 -2630.8
## - NYJ             1      2.63 24940 -2629.8
## - CHI             1      2.85 24940 -2629.6
## - cold_weather    1      3.27 24940 -2629.1
## - avg_fuml_plyr   1   1370.76 26308 -1162.0
## 
## Step:  AIC=-2632.51
## fuml ~ height + cold_weather + home_team_1 + ARI + BAL + CHI + 
##     CIN + IND + NE + NOR + NYG + NYJ + PHI + SEA + TEN + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - ARI             1      0.20 24938 -2634.3
## - home_team_1     1      0.27 24938 -2634.2
## - avg_rbry_pos    1      0.33 24938 -2634.1
## - BAL             1      0.34 24938 -2634.1
## - SEA             1      0.37 24938 -2634.1
## - height          1      0.38 24938 -2634.1
## - PHI             1      0.49 24938 -2634.0
## - NYG             1      0.56 24938 -2633.9
## - avg_qbtdp_plyr  1      0.78 24938 -2633.7
## - TEN             1      0.80 24938 -2633.6
## - CIN             1      0.93 24938 -2633.5
## - grass_1         1      1.40 24939 -2633.0
## - NE              1      1.54 24939 -2632.8
## - NOR             1      1.61 24939 -2632.7
## - IND             1      1.72 24939 -2632.6
## <none>                        24937 -2632.5
## - NYJ             1      2.57 24940 -2631.7
## - CHI             1      2.78 24940 -2631.4
## - cold_weather    1      3.29 24941 -2630.9
## - avg_fuml_plyr   1   1370.61 26308 -1164.0
## 
## Step:  AIC=-2634.28
## fuml ~ height + cold_weather + home_team_1 + BAL + CHI + CIN + 
##     IND + NE + NOR + NYG + NYJ + PHI + SEA + TEN + avg_rbry_pos + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - home_team_1     1      0.22 24938 -2636.0
## - BAL             1      0.32 24938 -2635.9
## - avg_rbry_pos    1      0.33 24938 -2635.9
## - height          1      0.37 24938 -2635.9
## - SEA             1      0.40 24938 -2635.8
## - PHI             1      0.51 24938 -2635.7
## - NYG             1      0.60 24938 -2635.6
## - avg_qbtdp_plyr  1      0.77 24938 -2635.4
## - TEN             1      0.77 24938 -2635.4
## - CIN             1      0.88 24938 -2635.3
## - grass_1         1      1.32 24939 -2634.8
## - NE              1      1.49 24939 -2634.6
## - NOR             1      1.54 24939 -2634.6
## - IND             1      1.65 24939 -2634.5
## <none>                        24938 -2634.3
## - NYJ             1      2.50 24940 -2633.5
## - CHI             1      2.72 24940 -2633.3
## - cold_weather    1      3.30 24941 -2632.7
## - avg_fuml_plyr   1   1370.41 26308 -1166.0
## 
## Step:  AIC=-2636.04
## fuml ~ height + cold_weather + BAL + CHI + CIN + IND + NE + NOR + 
##     NYG + NYJ + PHI + SEA + TEN + avg_rbry_pos + avg_fuml_plyr + 
##     avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_rbry_pos    1      0.34 24938 -2637.7
## - BAL             1      0.35 24938 -2637.7
## - SEA             1      0.36 24938 -2637.6
## - height          1      0.37 24938 -2637.6
## - PHI             1      0.49 24938 -2637.5
## - NYG             1      0.56 24938 -2637.4
## - avg_qbtdp_plyr  1      0.76 24939 -2637.2
## - TEN             1      0.80 24939 -2637.2
## - CIN             1      0.94 24939 -2637.0
## - NOR             1      1.51 24939 -2636.4
## - IND             1      1.58 24939 -2636.3
## - NE              1      1.59 24939 -2636.3
## - grass_1         1      1.67 24939 -2636.2
## <none>                        24938 -2636.0
## - NYJ             1      2.60 24940 -2635.2
## - CHI             1      2.76 24941 -2635.0
## - cold_weather    1      3.17 24941 -2634.6
## - avg_fuml_plyr   1   1370.19 26308 -1168.0
## 
## Step:  AIC=-2637.67
## fuml ~ height + cold_weather + BAL + CHI + CIN + IND + NE + NOR + 
##     NYG + NYJ + PHI + SEA + TEN + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - height          1      0.15 24938 -2639.5
## - BAL             1      0.34 24938 -2639.3
## - SEA             1      0.35 24938 -2639.3
## - PHI             1      0.47 24939 -2639.2
## - NYG             1      0.57 24939 -2639.0
## - avg_qbtdp_plyr  1      0.81 24939 -2638.8
## - TEN             1      0.82 24939 -2638.8
## - CIN             1      0.95 24939 -2638.6
## - NOR             1      1.48 24940 -2638.0
## - NE              1      1.58 24940 -2637.9
## - IND             1      1.63 24940 -2637.9
## - grass_1         1      1.68 24940 -2637.8
## <none>                        24938 -2637.7
## - NYJ             1      2.63 24941 -2636.8
## - CHI             1      2.78 24941 -2636.6
## - cold_weather    1      3.17 24941 -2636.2
## - avg_fuml_plyr   1   1465.76 26404 -1070.0
## 
## Step:  AIC=-2639.5
## fuml ~ cold_weather + BAL + CHI + CIN + IND + NE + NOR + NYG + 
##     NYJ + PHI + SEA + TEN + avg_fuml_plyr + avg_qbtdp_plyr + 
##     grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - BAL             1      0.33 24939 -2641.1
## - SEA             1      0.33 24939 -2641.1
## - PHI             1      0.46 24939 -2641.0
## - NYG             1      0.58 24939 -2640.9
## - avg_qbtdp_plyr  1      0.67 24939 -2640.8
## - TEN             1      0.82 24939 -2640.6
## - CIN             1      0.95 24939 -2640.4
## - NOR             1      1.52 24940 -2639.8
## - NE              1      1.64 24940 -2639.7
## - IND             1      1.66 24940 -2639.7
## - grass_1         1      1.69 24940 -2639.6
## <none>                        24938 -2639.5
## - NYJ             1      2.63 24941 -2638.6
## - CHI             1      2.74 24941 -2638.5
## - cold_weather    1      3.16 24941 -2638.0
## - avg_fuml_plyr   1   1506.14 26444 -1029.8
## 
## Step:  AIC=-2641.14
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYG + NYJ + 
##     PHI + SEA + TEN + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - SEA             1      0.38 24939 -2642.7
## - PHI             1      0.50 24939 -2642.6
## - NYG             1      0.63 24939 -2642.4
## - avg_qbtdp_plyr  1      0.70 24939 -2642.4
## - TEN             1      0.78 24939 -2642.3
## - CIN             1      0.89 24940 -2642.2
## - NOR             1      1.44 24940 -2641.6
## - NE              1      1.55 24940 -2641.4
## - IND             1      1.58 24940 -2641.4
## - grass_1         1      1.60 24940 -2641.4
## <none>                        24939 -2641.1
## - NYJ             1      2.54 24941 -2640.3
## - CHI             1      2.66 24941 -2640.2
## - cold_weather    1      3.04 24942 -2639.8
## - avg_fuml_plyr   1   1508.77 26447 -1028.7
## 
## Step:  AIC=-2642.72
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYG + NYJ + 
##     PHI + TEN + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - PHI             1      0.47 24939 -2644.2
## - NYG             1      0.58 24940 -2644.1
## - avg_qbtdp_plyr  1      0.68 24940 -2644.0
## - TEN             1      0.82 24940 -2643.8
## - CIN             1      0.97 24940 -2643.7
## - NOR             1      1.54 24941 -2643.0
## - NE              1      1.67 24941 -2642.9
## - IND             1      1.68 24941 -2642.9
## <none>                        24939 -2642.7
## - grass_1         1      1.82 24941 -2642.7
## - NYJ             1      2.66 24942 -2641.8
## - CHI             1      2.74 24942 -2641.7
## - cold_weather    1      3.21 24942 -2641.2
## - avg_fuml_plyr   1   1508.81 26448 -1030.3
## 
## Step:  AIC=-2644.21
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYG + NYJ + 
##     TEN + avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - NYG             1      0.54 24940 -2645.6
## - avg_qbtdp_plyr  1      0.71 24940 -2645.4
## - TEN             1      0.88 24940 -2645.2
## - CIN             1      1.02 24940 -2645.1
## - NOR             1      1.60 24941 -2644.4
## - NE              1      1.73 24941 -2644.3
## - grass_1         1      1.73 24941 -2644.3
## - IND             1      1.74 24941 -2644.3
## <none>                        24939 -2644.2
## - NYJ             1      2.75 24942 -2643.2
## - CHI             1      2.85 24942 -2643.1
## - cold_weather    1      3.26 24943 -2642.6
## - avg_fuml_plyr   1   1515.63 26455 -1024.7
## 
## Step:  AIC=-2645.61
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYJ + TEN + 
##     avg_fuml_plyr + avg_qbtdp_plyr + grass_1
## 
##                  Df Sum of Sq   RSS     AIC
## - avg_qbtdp_plyr  1      0.70 24941 -2646.8
## - TEN             1      0.92 24941 -2646.6
## - CIN             1      1.10 24941 -2646.4
## - NOR             1      1.70 24942 -2645.7
## <none>                        24940 -2645.6
## - IND             1      1.85 24942 -2645.6
## - NE              1      1.85 24942 -2645.6
## - grass_1         1      1.96 24942 -2645.4
## - NYJ             1      2.89 24943 -2644.4
## - CHI             1      2.94 24943 -2644.4
## - cold_weather    1      3.42 24943 -2643.8
## - avg_fuml_plyr   1   1515.79 26456 -1026.0
## 
## Step:  AIC=-2646.83
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYJ + TEN + 
##     avg_fuml_plyr + grass_1
## 
##                 Df Sum of Sq   RSS      AIC
## - TEN            1      0.89 24942 -2647.85
## - CIN            1      1.11 24942 -2647.61
## - NOR            1      1.81 24943 -2646.84
## <none>                       24941 -2646.83
## - IND            1      1.88 24943 -2646.76
## - grass_1        1      1.95 24943 -2646.69
## - NE             1      2.02 24943 -2646.61
## - NYJ            1      2.81 24944 -2645.74
## - CHI            1      2.88 24944 -2645.66
## - cold_weather   1      3.41 24944 -2645.08
## - avg_fuml_plyr  1   2528.17 27469     4.81
## 
## Step:  AIC=-2647.85
## fuml ~ cold_weather + CHI + CIN + IND + NE + NOR + NYJ + avg_fuml_plyr + 
##     grass_1
## 
##                 Df Sum of Sq   RSS      AIC
## - CIN            1      1.06 24943 -2648.68
## - NOR            1      1.72 24943 -2647.95
## - IND            1      1.81 24943 -2647.86
## <none>                       24942 -2647.85
## - NE             1      1.94 24944 -2647.71
## - grass_1        1      2.16 24944 -2647.46
## - NYJ            1      2.71 24944 -2646.86
## - CHI            1      2.75 24944 -2646.81
## - cold_weather   1      3.49 24945 -2646.00
## - avg_fuml_plyr  1   2527.57 27469     3.11
## 
## Step:  AIC=-2648.68
## fuml ~ cold_weather + CHI + IND + NE + NOR + NYJ + avg_fuml_plyr + 
##     grass_1
## 
##                 Df Sum of Sq   RSS      AIC
## - NOR            1      1.61 24944 -2648.92
## - IND            1      1.69 24944 -2648.83
## - NE             1      1.80 24944 -2648.70
## <none>                       24943 -2648.68
## - grass_1        1      1.89 24945 -2648.60
## - NYJ            1      2.56 24945 -2647.86
## - CHI            1      2.65 24945 -2647.76
## - cold_weather   1      3.30 24946 -2647.05
## - avg_fuml_plyr  1   2527.03 27470     1.63
## 
## Step:  AIC=-2648.92
## fuml ~ cold_weather + CHI + IND + NE + NYJ + avg_fuml_plyr + 
##     grass_1
## 
##                 Df Sum of Sq   RSS      AIC
## - IND            1      1.54 24946 -2649.22
## - grass_1        1      1.58 24946 -2649.17
## - NE             1      1.65 24946 -2649.10
## <none>                       24944 -2648.92
## - NYJ            1      2.38 24947 -2648.29
## - CHI            1      2.54 24947 -2648.12
## - cold_weather   1      3.51 24948 -2647.05
## - avg_fuml_plyr  1   2528.54 27473     2.74
## 
## Step:  AIC=-2649.22
## fuml ~ cold_weather + CHI + NE + NYJ + avg_fuml_plyr + grass_1
## 
##                 Df Sum of Sq   RSS      AIC
## - grass_1        1      1.31 24947 -2649.78
## - NE             1      1.52 24947 -2649.55
## <none>                       24946 -2649.22
## - NYJ            1      2.23 24948 -2648.77
## - CHI            1      2.44 24948 -2648.54
## - cold_weather   1      3.56 24949 -2647.30
## - avg_fuml_plyr  1   2527.83 27474     1.57
## 
## Step:  AIC=-2649.78
## fuml ~ cold_weather + CHI + NE + NYJ + avg_fuml_plyr
## 
##                 Df Sum of Sq   RSS      AIC
## - NE             1      1.25 24948 -2650.40
## <none>                       24947 -2649.78
## - NYJ            1      1.94 24949 -2649.64
## - CHI            1      2.69 24950 -2648.81
## - cold_weather   1      3.26 24950 -2648.18
## - avg_fuml_plyr  1   2526.94 27474    -0.01
## 
## Step:  AIC=-2650.4
## fuml ~ cold_weather + CHI + NYJ + avg_fuml_plyr
## 
##                 Df Sum of Sq   RSS      AIC
## <none>                       24948 -2650.40
## - NYJ            1      1.84 24950 -2650.38
## - CHI            1      2.57 24951 -2649.57
## - cold_weather   1      2.99 24951 -2649.10
## - avg_fuml_plyr  1   2532.79 27481     5.09

Conclusions

Rushing and passing data seems to be something that linear regression has better predictions for that receiving. This makes sense. RB’s and QB’s are generally singular players on the field. Both are heavily invested in by teams and are given a lot of touches every game. Receiving is a little more spread out. There are generally at minimum, 3 players in a receiving capacity (excluding the RB), 2 WR and a TE. There can be up to 4 WR on the field, so trying to predict who gets the ball will be harder because it is more uncertain.

RB’s are negatively effected by age, the data supports this well known fact, I was glad to see that relationship.

Fumbles and INTs are also going to be hard to predict because they are generally random, but highly dependent upon the player carrying the ball and the defense they are playing against.

The data seems to have some skewness, so I may have to explore other options for predicting.

Going forward, I would like to explore more fields, I have completely ignored the opponents in this analysis, and would like to add them in for the future.

As mentioned above, baseball will be better for predicting because of the nature of the game: One batter vs one pitcher. I would like to build an analysis for baseball based on a similar method as I have used for this.

Appendix

Charts

WR targets by avg yards per player

ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
  geom_point()+
  geom_text(data = subset(nfl_data, avg_recy_plyr > 75), aes(label = pname), size = 2.5)

There are few anomalies in this graph, not surprising, the amount of targets correlates with the amount of yards a player gets. The top right corner is “ALL PRO” corner.

**Tight ends should not be compared to WR

ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
  geom_point(data = subset(nfl_data, pos1 == "TE"))+
  geom_text(data = subset(nfl_data, avg_recy_plyr > 50 & pos1 == "TE"), aes(label = pname), size = 2.5)

I separated out the TE from the WR. TE are not “homerun” hitters, but are frequent targets of QB’s. Rob Gronkowski is the biggest anomaly here, he is widely considered the best position player to ever play.

** RB’s separated out

ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
  geom_point(data = subset(nfl_data, pos1 == "RB"))+
  geom_text(data = subset(nfl_data, avg_recy_plyr > 30 & pos1 == "RB"), aes(label = pname), size = 2.5)

CJ prosise was a rookie who had a couple of explosive games. He is a RB who played WR in college. He switched to RB his senior year of college and became an elite RB. This trend will regress somewhat, however, he is a very legit dual threat.

**WR only

ggplot(data = nfl_data, aes(x = avg_recy_plyr, y = avg_trg_plyr, col = Teams ))+
  geom_point(data = subset(nfl_data, pos1 == "WR"))+
  geom_text(data = subset(nfl_data, avg_recy_plyr > 70 & pos1 == "WR"), aes(label = pname), size = 2.5)